<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg1.png"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls11 ws0">EA<span class="_0 blank"></span>E0<span class="_0 blank"></span>207<span class="_0 blank"></span>:<span class="_1 blank"> </span>M<span class="_0 blank"></span>ate<span class="_0 blank"></span>mát<span class="_0 blank"></span>ica A<span class="_0 blank"></span>pli<span class="_0 blank"></span>cad<span class="_0 blank"></span>a à Eco<span class="_0 blank"></span>no<span class="_0 blank"></span>mia</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls11 ws1">Aula 3:<span class="_2 blank"> </span>P<span class="_0 blank"></span>osto - O Critério Fundamental</div><div class="t m0 x3 h4 y4 ff1 fs1 fc1 sc0 ls11 ws2">Ma<span class="_0 blank"></span>rcos Y. Nakaguma</div><div class="t m0 x4 h4 y5 ff1 fs1 fc1 sc0 ls11 ws3">09/08/2017</div><div class="t m0 x5 h5 y6 ff1 fs2 fc1 sc0 ls11">1</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls11 ws4">Re<span class="_0 blank"></span>vis<span class="_0 blank"></span>ão</div><div class="t m0 x7 h4 y9 ff1 fs1 fc1 sc0 ls11 ws5">Na aula passada, iniciamos o nosso estudo sob<span class="_0 blank"></span>re sistemas de equações</div><div class="t m0 x7 h4 ya ff1 fs1 fc1 sc0 ls11 ws1">linea<span class="_0 blank"></span>res.<span class="_2 blank"> </span>Discutimos os seguintes temas:</div><div class="t m0 x8 h6 yb ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc2 ls11 ws6 v1">Méto<span class="_3 blank"> </span>dos de resolução de sistemas linea<span class="_0 blank"></span>res:</span></div><div class="t m0 x9 h7 yc ff1 fs5 fc0 sc0 ls1">1<span class="ff3 ls2">.</span><span class="fc1 ls11 ws7">Su b st i t u iç ã o ;</span></div><div class="t m0 x9 h7 yd ff1 fs5 fc0 sc0 ls1">2<span class="ff3 ls2">.</span><span class="fc1 ls11 ws8">Eli m i n a ç ã o<span class="_4 blank"> </span>de<span class="_4 blank"> </span>variáv e is<span class="_4 blank"> </span>(i. e.<span class="_5 blank"> </span>elim<span class="_3 blank"> </span>in a ç ã o<span class="_4 blank"> </span>de<span class="_4 blank"> </span>Ga u ss - J orda n ) .</span></div><div class="t m0 x9 h7 ye ff1 fs5 fc0 sc0 ls1">3<span class="ff3 ls2">.</span><span class="fc1 ls11 ws9">Mé t o<span class="_6 blank"> </span>dos<span class="_4 blank"> </span>M a tr i c ia i s<span class="_4 blank"> </span>(Re g r a<span class="_4 blank"> </span>de<span class="_4 blank"> </span>Cra m<span class="_3 blank"> </span>e r)</span></div><div class="t m0 x8 h8 yf ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc2 ls11 wsa v1">Classi\u2026cação de sistemas com relação ao número de soluções:</span></div><div class="t m0 x9 h7 y10 ff1 fs5 fc0 sc0 ls1">1<span class="ff3 ls2">.</span><span class="fc1 ls11 ws9">Sis t e m a s<span class="_4 blank"> </span>co m<span class="_4 blank"> </span>um<span class="_3 blank"> </span>a<span class="_4 blank"> </span>úni c a<span class="_4 blank"> </span>sol u ç ã o ;</span></div><div class="t m0 x9 h7 y11 ff1 fs5 fc0 sc0 ls1">2<span class="ff3 ls2">.</span><span class="fc1 ls11 ws9">Sis t e m a s<span class="_4 blank"> </span>co m<span class="_4 blank"> </span>vá r ia s<span class="_4 blank"> </span>(in \u2026 n i t a s )<span class="_4 blank"> </span>solu ç õ e s ;</span></div><div class="t m0 x9 h7 y12 ff1 fs5 fc0 sc0 ls1">3<span class="ff3 ls2">.</span><span class="fc1 ls11 wsb">Sis t e m a s<span class="_4 blank"> </span>se m<span class="_4 blank"> </span>so lu ç ã o .</span></div><div class="t m0 x5 h5 y13 ff1 fs2 fc1 sc0 ls11">2</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 wsc">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>as d<span class="_0 blank"></span>e Equ<span class="_0 blank"></span>aç<span class="_0 blank"></span>ões Li<span class="_0 blank"></span>nea<span class="_7 blank"></span>re<span class="_0 blank"></span>s:<span class="_1 blank"> </span>Ca<span class="_0 blank"></span>so G<span class="_0 blank"></span>eral 2<span class="_0 blank"></span>x2</div><div class="t m0 x7 h4 y16 ff1 fs1 fc1 sc0 ls11 wsd">Considere o seguinte sistema com duas equações e duas incógnitas:</div><div class="t m0 xa h9 y17 ff4 fs1 fc1 sc0 ls3">\ue01a<span class="ff5 ls4 v2">a</span><span class="ff1 fs2 ls11 wse v3">11<span class="_8 blank"> </span></span><span class="ff5 ls5 v2">x</span><span class="ff1 fs2 ls6 v3">1</span><span class="ff6 fs6 ls7 v2">+</span><span class="ff5 ls4 v2">a</span><span class="ff1 fs2 ls11 wse v3">12<span class="_8 blank"> </span></span><span class="ff5 ls11 ws3 v2">x</span><span class="ff1 fs2 ls8 v3">2</span><span class="ff6 fs6 ls9 v2">=</span><span class="ff5 ls11 ws3 v2">b<span class="ff1 fs2 v1">1</span></span></div><div class="t m0 xb ha y18 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 wse v1">21<span class="_8 blank"> </span></span><span class="ls5">x<span class="ff1 fs2 lsa v1">1</span><span class="ff6 fs6 ls7 v0">+</span></span><span class="v0">a<span class="ff1 fs2 ls11 wse v1">22<span class="_8 blank"> </span></span><span class="ls11 ws3">x<span class="ff1 fs2 ls8 v1">2</span><span class="ff6 fs6 ls9">=</span>b<span class="ff1 fs2 v1">2</span></span></span></div><div class="t m0 x7 h4 y19 ff1 fs1 fc1 sc0 ls11 wsf">onde assume-se os pa<span class="_0 blank"></span>râmetros <span class="ff5 lsb">a</span><span class="fs2 wse v1">1 1<span class="_8 blank"> </span></span><span class="ff7 lsc">,<span class="ff5 lsd">a</span></span><span class="fs2 wse v1">12<span class="_8 blank"> </span></span><span class="lse">,<span class="ff5 lsf">a</span></span><span class="fs2 wse v1">21<span class="_5 blank"> </span></span><span class="ls10">e<span class="ff5 lsd">a</span></span><span class="fs2 wse v1">2 2<span class="_5 blank"> </span></span><span class="wsd">são estritamente</span></div><div class="t m0 x7 h4 y1a ff1 fs1 fc1 sc0 ls11 ws10">p ositivos.</div><div class="t m0 x7 h4 y1b ff1 fs1 fc1 sc0 ls11 wsf">P<span class="_0 blank"></span>o<span class="_3 blank"> </span>demos resolver este sistema através do <span class="fc2 ws11">mé to do<span class="_4 blank"> </span>da<span class="_9 blank"> </span>substituição</span>.</div><div class="t m0 x5 h5 y1c ff1 fs2 fc1 sc0 ls11">3</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg2.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y1d ff1 fs0 fc0 sc0 ls11 ws13">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>as d<span class="_0 blank"></span>e Equ<span class="_0 blank"></span>aç<span class="_0 blank"></span>ões Li<span class="_0 blank"></span>nea<span class="_7 blank"></span>re<span class="_0 blank"></span>s:<span class="_1 blank"> </span>Ca<span class="_0 blank"></span>so G<span class="_0 blank"></span>eral 2<span class="_0 blank"></span>x2</div><div class="t m0 x7 h4 y1e ff1 fs1 fc2 sc0 ls11 wsd">P<span class="_0 blank"></span>asso 1<span class="fc1 wsf">:<span class="_2 blank"> </span>Resolva a primeira equação pa<span class="_0 blank"></span>ra <span class="ff5 ls12">x</span><span class="fs2 ls13 v1">1</span>:</span></div><div class="t m0 xc hb y1f ff5 fs1 fc1 sc0 ls11 ws3">x<span class="ff1 fs2 ls14 v1">1</span><span class="ff6 fs6 ls15 v0">+</span><span class="lsf v4">a</span><span class="ff1 fs2 ws14 v5">12</span></div><div class="t m0 xd hc y20 ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 ws15 v1">11</span></div><div class="t m0 xe hd y21 ff5 fs1 fc1 sc0 ls12">x<span class="ff1 fs2 ls16 v1">2</span><span class="ff6 fs6 ls17 v0">=</span><span class="ls11 ws3 v4">b<span class="ff1 fs2 v1">1</span></span></div><div class="t m0 xf hc y20 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v1">11</span></div><div class="t m0 x10 he y22 ff8 fs6 fc1 sc0 ls18">!<span class="ff5 fs1 ls12">x<span class="ff1 fs2 ls19 v1">1</span></span><span class="ff6 ls17">=<span class="ff5 fs1 ls11 ws3 v4">b<span class="ff1 fs2 v1">1</span></span></span></div><div class="t m0 x11 hc y20 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 wse v1">11</span></div><div class="t m0 x12 he y22 ff8 fs6 fc1 sc0 ls15">\ue000<span class="ff5 fs1 lsd v4">a</span><span class="ff1 fs2 ls11 wse v5">12</span></div><div class="t m0 x13 hc y20 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v1">11</span></div><div class="t m0 x14 hc y21 ff5 fs1 fc1 sc0 ls12">x<span class="ff1 fs2 ls11 v1">2</span></div><div class="t m0 x7 h4 y23 ff1 fs1 fc2 sc0 ls11 wsd">P<span class="_0 blank"></span>asso 2<span class="fc1">:<span class="_2 blank"> </span>Substituir a expressão acima na segunda equação e resolver</span></div><div class="t m0 x7 h4 y24 ff1 fs1 fc1 sc0 ls11 ws16">pa<span class="_0 blank"></span>ra <span class="ff5 ws3">x</span><span class="fs2 ls1a v1">2</span>:</div><div class="t m0 x15 hf y25 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 ws14 v1">21<span class="_a blank"> </span></span><span class="ff4 ls1b v6">\ue012</span><span class="ls11 ws3 v4">b<span class="ff1 fs2 v1">1</span></span></div><div class="t m0 x16 hc y26 ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 wse v1">11</span></div><div class="t m0 x17 h10 y27 ff8 fs6 fc1 sc0 ls1c">\ue000<span class="ff5 fs1 lsf v4">a</span><span class="ff1 fs2 ls11 wse v5">12</span></div><div class="t m0 x18 hc y26 ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 wse v1">11</span></div><div class="t m0 x10 hf y28 ff5 fs1 fc1 sc0 ls11 ws3">x<span class="ff1 fs2 ls1d v1">2</span><span class="ff4 ls1e v6">\ue013</span><span class="ff6 fs6 ls7 v0">+</span><span class="lsf v0">a</span><span class="ff1 fs2 wse v1">22<span class="_8 blank"> </span></span><span class="v0">x<span class="ff1 fs2 ls1f v1">2</span><span class="ff6 fs6 ls9">=</span>b<span class="ff1 fs2 v1">2</span></span></div><div class="t m0 x19 h11 y29 ff8 fs6 fc1 sc0 ls20">!<span class="ff6 ls21 v0">(</span><span class="ff5 fs1 lsf">a<span class="ff1 fs2 ls11 wse v1">11<span class="_8 blank"> </span></span><span class="lsd">a<span class="ff1 fs2 ls11 wse v1">22<span class="_4 blank"> </span></span></span></span><span class="ls7">\ue000<span class="ff5 fs1 lsf">a<span class="ff1 fs2 ls11 wse v1">12<span class="_8 blank"> </span></span><span class="lsd">a<span class="ff1 fs2 ls11 wse v1">21<span class="_8 blank"> </span></span></span></span><span class="ff6 ls22 v0">)</span><span class="ff5 fs1 ls12">x<span class="ff1 fs2 ls19 v1">2</span></span><span class="ff6 ls23">=<span class="ls24 v0">(</span><span class="ff5 fs1 lsf">a<span class="ff1 fs2 ls11 wse v1">1 1<span class="_6 blank"> </span></span><span class="ls11 ws3">b<span class="ff1 fs2 ls14 v1">2</span></span></span></span><span class="ls25">\ue000<span class="ff5 fs1 ls4">a<span class="ff1 fs2 ls11 wse v1">2 1<span class="_8 blank"> </span></span><span class="ls11 ws3">b<span class="ff1 fs2 ls26 v1">1</span><span class="ff6 fs6 v0">)</span></span></span></span></span></div><div class="t m0 x5 h5 y2a ff1 fs2 fc1 sc0 ls11">4</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls11 wsc">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>as d<span class="_0 blank"></span>e Equ<span class="_0 blank"></span>aç<span class="_0 blank"></span>ões Li<span class="_0 blank"></span>nea<span class="_7 blank"></span>re<span class="_0 blank"></span>s:<span class="_1 blank"> </span>Ca<span class="_0 blank"></span>so G<span class="_0 blank"></span>eral 2<span class="_0 blank"></span>x2</div><div class="t m0 x7 h4 y2b ff1 fs1 fc1 sc0 ls11 ws11">Note<span class="_9 blank"> </span>que<span class="_4 blank"> </span>existem<span class="_9 blank"> </span>três<span class="_4 blank"> </span>p ossibilidades:</div><div class="t m0 x1a h12 y2c ff5 fs4 fc0 sc0 ls27">i<span class="ff7 ls28">.<span class="ff1 fc1 ls11 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls2a">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls2d">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff8 fs7 ls2e">6<span class="ff6 ls2f">=</span></span><span class="ws18">0, então po<span class="_3 blank"> </span>demos utilizar as exp<span class="_0 blank"></span>ressões acima</span></span></span></div><div class="t m0 x1b h13 y2d ff1 fs4 fc1 sc0 ls11 ws19">pa<span class="_0 blank"></span>ra <span class="fc2 ws1a v0">resolver <span class="fc1 ws1b">para <span class="ff5 ws1c">x</span><span class="fs2 ls30 v7">1</span><span class="ls31">e</span><span class="ff5 ws1c">x</span><span class="fs2 ls32 v7">2</span><span class="ws1d">.<span class="_5 blank"> </span>Neste caso, o sistema possui uma </span></span><span class="ws1c">única</span></span></div><div class="t m0 x1b h13 y2e ff1 fs4 fc2 sc0 ls11 ws1c">solução<span class="fc1 v0">.</span></div><div class="t m0 x1c h12 y2f ff5 fs4 fc0 sc0 ls11 ws1e">ii <span class="ff7 ls33">.</span><span class="ff1 fc1 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls2a">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls34">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls2d">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs7 ls35">=</span><span class="wsa">0 e <span class="ff5 ls36">a</span><span class="fs2 wse v7">11<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls37 v7">2</span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls38 v7">1</span><span class="ff6 fs7 ls39">=</span><span class="ws1d">0, então <span class="fc2 ws6">as duas equações</span></span></span></span></div><div class="t m0 x1b h13 y30 ff1 fs4 fc2 sc0 ls11 ws1d">são idênticas<span class="fc1 ws1f v0">.<span class="_5 blank"> </span>(Prove!)<span class="_5 blank"> </span>Neste caso, o sistema p<span class="_3 blank"> </span>ossui <span class="fc2 ws20">in\u2026nitas soluções</span>.</span></div><div class="t m0 x1d h12 y31 ff5 fs4 fc0 sc0 ls11 ws21">iii <span class="ff7 ls3a">.</span><span class="ff1 fc1 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls2a">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls34">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls2d">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs7 ls35">=</span><span class="ws1d">0 e <span class="ff5 ls36">a</span><span class="fs2 wse v7">11<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls37 v7">2</span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls38 v7">1</span><span class="ff8 fs7 ls2e">6<span class="ff6 ls39">=</span></span>0, então <span class="fc2 ws6">as duas equações</span></span></span></div><div class="t m0 x1b h14 y32 ff1 fs4 fc2 sc0 ls11 ws1d">são incompatíveis<span class="fc1 v0">.<span class="_5 blank"> </span>Neste caso, o sistema <span class="fc2 ws22">não<span class="_4 blank"> </span>p ossui<span class="_4 blank"> </span>solução</span>.</span></div><div class="t m0 x5 h5 y33 ff1 fs2 fc1 sc0 ls11">5</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 ws4">Pr<span class="_0 blank"></span>ova</div><div class="t m0 x7 h11 y34 ff1 fs1 fc2 sc0 ls11 ws23">Prop osição:<span class="_2 blank"> </span><span class="fc1 ws10">Sup onha<span class="_9 blank"> </span>q<span class="_0 blank"></span>ue<span class="_9 blank"> </span><span class="ff5 lsf">a</span><span class="fs2 wse v7">11<span class="_8 blank"> </span></span><span class="ff5 lsf">a</span><span class="fs2 wse v7">22<span class="_4 blank"> </span></span><span class="ff8 fs6 ls7">\ue000</span><span class="ff5 lsf">a</span><span class="fs2 wse v7">12<span class="_8 blank"> </span></span><span class="ff5 lsd">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs6 ls3b">=</span><span class="wsd">0 e <span class="ff5 ls4">a</span><span class="fs2 wse v7">1 1<span class="_8 blank"> </span></span><span class="ff5 ws3">b</span><span class="fs2 ls3c v7">2</span><span class="ff8 fs6 ls7">\ue000</span><span class="ff5 lsf">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ws3">b</span><span class="fs2 ls3d v7">1</span><span class="ff6 fs6 ls9">=</span>0.</span></span></div><div class="t m0 x7 h4 y35 ff1 fs1 fc1 sc0 ls11 wsf">Prove que as duas equações do sistema são idênticas, ie.<span class="_2 blank"> </span>rep<span class="_0 blank"></span>resentam</div><div class="t m0 x7 h4 y36 ff1 fs1 fc1 sc0 ls11 ws24">retas pa<span class="_0 blank"></span>ralelas coincidentes<span class="ff7">.</span></div><div class="t m0 x7 h4 y37 ff1 fs1 fc2 sc0 ls11 ws25">Prova: <span class="fc1 wsf">Observe que as condições dadas fo<span class="_0 blank"></span>rmam o seguinte sistema:</span></div><div class="t m0 x1e h15 y38 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 wse v7">11<span class="_8 blank"> </span></span><span class="lsf">a<span class="ff1 fs2 ls11 wse v7">22<span class="_4 blank"> </span></span><span class="ff8 fs6 ls7 v0">\ue000</span></span><span class="v0">a<span class="ff1 fs2 ls11 wse v7">12<span class="_8 blank"> </span></span><span class="lsf">a<span class="ff1 fs2 ls11 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs6 ls3b">=</span><span class="ff1 ls11">0</span></span></span></div><div class="t m0 x1f h11 y39 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v7">11<span class="_8 blank"> </span></span><span class="ls11 ws3">b<span class="ff1 fs2 ls3e v7">2</span><span class="ff8 fs6 ls7">\ue000</span><span class="ls4">a</span><span class="ff1 fs2 ws14 v7">21<span class="_8 blank"> </span></span>b<span class="ff1 fs2 ls3f v7">1</span><span class="ff6 fs6 ls9">=</span><span class="ff1">0</span></span></div><div class="t m0 x7 h4 y3a ff1 fs1 fc1 sc0 ls11 ws26">Resolvendo pa<span class="_0 blank"></span>ra <span class="ff5 lsf">a</span><span class="fs2 ws14 v7">2 1<span class="_5 blank"> </span></span><span class="ls40">e<span class="ff5 lsb">a</span></span><span class="fs2 wse v7">2 2<span class="_8 blank"> </span></span><span class="ws2">, obtemos:</span></div><div class="t m0 x20 h16 y3b ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 wse v7">21<span class="_5 blank"> </span></span><span class="ff6 fs6 ls41 v0">=</span><span class="lsf v4">a</span><span class="ff1 fs2 ls11 wse v5">11<span class="_6 blank"> </span></span><span class="ls11 ws3 v4">b<span class="ff1 fs2 v7">2</span></span></div><div class="t m0 x21 hc y3c ff5 fs1 fc1 sc0 ls11 ws3">b<span class="ff1 fs2 v7">1</span></div><div class="t m0 x22 h17 y3d ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 ws14 v7">22<span class="_5 blank"> </span><span class="ff6 fs6 v8">=</span></span></div><div class="t m0 x23 h18 y3e ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 wse v7">12<span class="_a blank"> </span></span><span class="ff4 ls42 v9">\ue010</span><span class="fs2 ls43 va">a</span><span class="ff1 fs8 ls11 ws27 vb">11<span class="_8 blank"> </span></span><span class="fs2 ls44 va">b</span><span class="ff1 fs8 ls11 vb">2</span></div><div class="t m0 x24 h19 y3f ff5 fs2 fc1 sc0 ls45">b<span class="ff1 fs8 ls46 vc">1</span><span class="ff4 fs1 ls11 vd">\ue011</span></div><div class="t m0 x25 hc y40 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v7">11</span></div><div class="t m0 x26 h1a y41 ff8 fs6 fc1 sc0 ls47">!<span class="ff5 fs1 ls4">a<span class="ff1 fs2 ls11 wse v7">22<span class="_5 blank"> </span></span></span><span class="ff6 ls41">=<span class="ff5 fs1 lsd v4">a</span><span class="ff1 fs2 ls11 wse v5">12<span class="_6 blank"> </span></span><span class="ff5 fs1 ls11 ws3 v4">b<span class="ff1 fs2 v7">2</span></span></span></div><div class="t m0 x12 hc y40 ff5 fs1 fc1 sc0 ls11 ws3">b<span class="ff1 fs2 v7">1</span></div><div class="t m0 x7 ha y42 ff1 fs1 fc1 sc0 ls11 ws28">Assim, substituíndo as exp<span class="_0 blank"></span>ressões ac<span class="_3 blank"> </span>ima em <span class="ff5 lsf">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ls48">x</span><span class="fs2 ls49 v7">1</span><span class="ff6 fs6 ls4a v0">+<span class="ff5 fs1 lsf">a</span></span><span class="fs2 wse v7">22<span class="_8 blank"> </span></span><span class="ff5 ws3 v0">x</span><span class="fs2 ls8 v7">2</span><span class="ff6 fs6 ls9 v0">=</span><span class="ff5 ws3 v0">b</span><span class="fs2 ls4b v7">2</span><span class="ws3 v0">temos</span></div><div class="t m0 x7 h4 y43 ff1 fs1 fc1 sc0 ls11 ws3">que:</div><div class="t m0 x27 hc y44 ff5 fs1 fc1 sc0 ls4">a<span class="ff1 fs2 ls11 ws14 v7">11<span class="_8 blank"> </span></span><span class="ls11 ws3">b<span class="ff1 fs2 v7">2</span></span></div><div class="t m0 x28 hc y45 ff5 fs1 fc1 sc0 ls11 ws3">b<span class="ff1 fs2 v7">1</span></div><div class="t m0 x29 h1b y46 ff5 fs1 fc1 sc0 ls12">x<span class="ff1 fs2 ls4c v7">1</span><span class="ff6 fs6 ls1c v0">+</span><span class="lsd v4">a</span><span class="ff1 fs2 ls11 wse v5">12<span class="_8 blank"> </span></span><span class="ls11 ws3 v4">b<span class="ff1 fs2 v7">2</span></span></div><div class="t m0 xe hc y45 ff5 fs1 fc1 sc0 ls11 ws3">b<span class="ff1 fs2 v7">1</span></div><div class="t m0 xb h1c y46 ff5 fs1 fc1 sc0 ls12">x<span class="ff1 fs2 ls4d v7">2</span><span class="ff6 fs6 ls9 v0">=</span><span class="ls11 ws3 v0">b<span class="ff1 fs2 ls4e v7">2</span><span class="ff8 fs6 ls4f">!</span><span class="lsd">a</span><span class="ff1 fs2 wse v7">11<span class="_8 blank"> </span></span>x<span class="ff1 fs2 ls50 v7">1</span><span class="ff6 fs6 ls7">+</span><span class="lsb">a</span><span class="ff1 fs2 wse v7">12<span class="_8 blank"> </span></span><span class="ls5">x<span class="ff1 fs2 ls51 v7">2</span><span class="ff6 fs6 ls9">=</span></span>b<span class="ff1 fs2 ls52 v7">1</span><span class="ff2 fs3 ve">\ue004</span></span></div><div class="t m0 x5 h5 y47 ff1 fs2 fc1 sc0 ls11">6</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg3.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y1d ff1 fs0 fc0 sc0 ls11 wsc">Si<span class="_0 blank"></span>stem<span class="_0 blank"></span>as d<span class="_0 blank"></span>e Equ<span class="_0 blank"></span>aç<span class="_0 blank"></span>ões Li<span class="_0 blank"></span>nea<span class="_7 blank"></span>re<span class="_0 blank"></span>s:<span class="_1 blank"> </span>Ca<span class="_0 blank"></span>so G<span class="_0 blank"></span>eral 2<span class="_0 blank"></span>x2</div><div class="t m0 x7 h4 y48 ff1 fs1 fc2 sc0 ls11">Resumo:</div><div class="t m0 x1a h12 y49 ff5 fs4 fc0 sc0 ls27">i<span class="ff7 ls28">.<span class="ff1 fc1 ls11 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls2a">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls2d">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff8 fs7 ls2e">6<span class="ff6 ls2f">=</span></span><span class="ws1d">0, então o sistema possui uma <span class="fc2 ws29">única solução</span></span></span></span></div><div class="t m0 x1b h1d y4a ff1 fs4 fc1 sc0 ls11 ws22">dada<span class="_4 blank"> </span>por:</div><div class="t m0 x29 h1e y4b ff5 fs4 fc1 sc0 ls11 ws1c">x<span class="ff1 fs2 ls53 v7">1</span><span class="ff6 fs7 ls54">=</span><span class="ls36 vf">a</span><span class="ff1 fs2 wse v10">22<span class="_8 blank"> </span></span><span class="vf">b</span><span class="ff1 fs2 ls55 v10">1</span><span class="ff8 fs7 ls2b vf">\ue000</span><span class="ls2c vf">a</span><span class="ff1 fs2 wse v10">12<span class="_8 blank"> </span></span><span class="vf">b</span><span class="ff1 fs2 v10">2</span></div><div class="t m0 x2a h12 y4c ff5 fs4 fc1 sc0 ls29">a<span class="ff1 fs2 ls11 wse v7">11<span class="_8 blank"> </span></span><span class="ls2c">a<span class="ff1 fs2 ls11 wse v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls2b">\ue000</span>a<span class="ff1 fs2 ls11 wse v7">1 2<span class="_8 blank"> </span></span><span class="ls36">a<span class="ff1 fs2 ls11 wse v7">21</span></span></span></div><div class="t m0 x21 h1e y4d ff1 fs4 fc1 sc0 ls56">e<span class="ff5 ls11 ws1c">x</span><span class="fs2 ls57 v7">2</span><span class="ff6 fs7 ls58">=</span><span class="ff5 ls59 vf">a</span><span class="fs2 ls11 wse v10">11<span class="_8 blank"> </span></span><span class="ff5 ls11 ws1c vf">b</span><span class="fs2 ls55 v10">2</span><span class="ff8 fs7 ls34 vf">\ue000</span><span class="ff5 ls36 vf">a</span><span class="fs2 ls11 wse v10">21<span class="_8 blank"> </span></span><span class="ff5 ls11 ws1c vf">b</span><span class="fs2 ls11 v10">1</span></div><div class="t m0 x2b h12 y4c ff5 fs4 fc1 sc0 ls2d">a<span class="ff1 fs2 ls11 wse v7">11<span class="_8 blank"> </span></span><span class="ls29">a<span class="ff1 fs2 ls11 wse v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls34">\ue000</span><span class="ls36">a<span class="ff1 fs2 ls11 wse v7">1 2<span class="_8 blank"> </span></span><span class="ls2c">a<span class="ff1 fs2 ls11 wse v7">21</span></span></span></span></div><div class="t m0 x1c h12 y4e ff5 fs4 fc0 sc0 ls11 ws1e">ii <span class="ff7 ls33">.</span><span class="ff1 fc1 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls59">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls59">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs7 ls35">=</span><span class="ws1d">0 e <span class="ff5 ls36">a</span><span class="fs2 wse v7">11<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls55 v7">2</span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls5a v7">1</span><span class="ff8 fs7 ls2e">6<span class="ff6 ls39">=</span></span>0, então o sistema <span class="fc2 ws1c">não</span></span></span></div><div class="t m0 x1b h1d y4f ff1 fs4 fc2 sc0 ls11 ws22">p ossui<span class="_4 blank"> </span>solução<span class="fc1">.</span></div><div class="t m0 x1d h12 y50 ff5 fs4 fc0 sc0 ls11 ws21">iii <span class="ff7 ls3a">.</span><span class="ff1 fc1 ws17">Se <span class="ff5 ls29">a</span><span class="fs2 ws14 v7">11<span class="_8 blank"> </span></span><span class="ff5 ls59">a</span><span class="fs2 ws14 v7">22<span class="_a blank"> </span></span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 ws14 v7">1 2<span class="_8 blank"> </span></span><span class="ff5 ls59">a</span><span class="fs2 wse v7">21<span class="_9 blank"> </span></span><span class="ff6 fs7 ls35">=</span><span class="ws1d">0 e <span class="ff5 ls36">a</span><span class="fs2 wse v7">11<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls55 v7">2</span><span class="ff8 fs7 ls2b">\ue000</span><span class="ff5 ls2c">a</span><span class="fs2 wse v7">21<span class="_8 blank"> </span></span><span class="ff5 ws1c">b</span><span class="fs2 ls5a v7">1</span><span class="ff6 fs7 ls39">=</span><span class="wsa">0, então o sistema possui</span></span></span></div><div class="t m0 x1b h1d y51 ff1 fs4 fc2 sc0 ls11 ws6">in\u2026nitas soluções <span class="fc1 ws2a">dadas<span class="_4 blank"> </span>por:</span></div><div class="t m0 x20 h1f y52 ff5 fs4 fc1 sc0 ls11 ws1c">x<span class="ff1 fs2 ls53 v7">1</span><span class="ff6 fs7 ls5b">=</span><span class="vf">b</span><span class="ff1 fs2 v10">1</span></div><div class="t m0 x2c h20 y53 ff5 fs4 fc1 sc0 ls2a">a<span class="ff1 fs2 ls11 wse v7">11</span></div><div class="t m0 x2d h21 y54 ff8 fs7 fc1 sc0 ls5c">\ue000<span class="ff5 fs4 ls2c vf">a</span><span class="ff1 fs2 ls11 wse v10">12</span></div><div class="t m0 x2e h20 y53 ff5 fs4 fc1 sc0 ls2c">a<span class="ff1 fs2 ls11 wse v7">11</span></div><div class="t m0 x2f h20 y54 ff5 fs4 fc1 sc0 ls5d">x<span class="ff1 fs2 ls11 v7">2</span></div><div class="t m0 x5 h5 y55 ff1 fs2 fc1 sc0 ls11">7</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x30 h22 y56 ff1 fs9 fc1 sc0 ls11 ws2b">S<span class="_7 blank"></span>is<span class="_0 blank"></span>t<span class="_0 blank"></span>e<span class="_0 blank"></span>m<span class="_7 blank"></span>a d<span class="_0 blank"></span>e E<span class="_7 blank"></span>q<span class="_0 blank"></span>u<span class="_0 blank"></span>a<span class="_0 blank"></span>ç<span class="_0 blank"></span>õ<span class="_0 blank"></span>e<span class="_0 blank"></span>s L<span class="_0 blank"></span>in<span class="_7 blank"></span>e<span class="_0 blank"></span>a<span class="_7 blank"></span>r<span class="_7 blank"></span>es<span class="_7 blank"></span>:</div><div class="t m0 x30 h22 y57 ff1 fs9 fc1 sc0 ls11 ws2c">M<span class="_7 blank"></span>a<span class="_7 blank"></span>t<span class="_0 blank"></span>ri<span class="_0 blank"></span>z d<span class="_7 blank"></span>e C<span class="_0 blank"></span>oe<span class="_0 blank"></span>\u2026<span class="_7 blank"></span>ci<span class="_0 blank"></span>e<span class="_0 blank"></span>n<span class="_7 blank"></span>te<span class="_7 blank"></span>s e<span class="_b blank"> </span>P<span class="_c blank"></span>o<span class="_7 blank"></span>st<span class="_7 blank"></span>o</div><div class="t m0 x5 h5 y13 ff1 fs2 fc1 sc0 ls11">8</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 ws2d">M<span class="_0 blank"></span>atr<span class="_0 blank"></span>iz<span class="_5 blank"> </span>de<span class="_5 blank"> </span>Coe\u2026c<span class="_0 blank"></span>ient<span class="_0 blank"></span>es</div><div class="t m0 x7 h4 y58 ff1 fs1 fc1 sc0 ls11 wsd">Dado o sistema de equações linea<span class="_0 blank"></span>res:</div><div class="t m0 x29 h9 y59 ff4 fs1 fc1 sc0 ls11">8</div><div class="t m0 x29 h9 y5a ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y5b ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y5c ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y5d ff4 fs1 fc1 sc0 ls11"><</div><div class="t m0 x29 h9 y5e ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y5f ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y60 ff4 fs1 fc1 sc0 ls11">></div><div class="t m0 x29 h9 y61 ff4 fs1 fc1 sc0 ls11">:</div><div class="t m0 x31 h23 y62 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v7">11<span class="_8 blank"> </span></span><span class="ls12">x<span class="ff1 fs2 ls5e v7">1</span><span class="ff6 fs6 ls7 v0">+</span></span><span class="v0">a<span class="ff1 fs2 ls11 wse v7">12<span class="_8 blank"> </span></span><span class="ls11 ws3">x<span class="ff1 fs2 ls5f v7">2</span><span class="ff6 fs6 ls7">+</span><span class="ff7 ws2e">... <span class="ff6 fs6 ls60">+</span></span></span>a<span class="ff1 fs2 ls61 v7">1<span class="ff5 ls62">n</span></span><span class="ls12">x<span class="fs2 ls63 v7">n</span><span class="ff6 fs6 ls9">=</span><span class="ls11 ws3">b<span class="ff1 fs2 v7">1</span></span></span></span></div><div class="t m0 x31 h24 y63 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 wse v7">21<span class="_8 blank"> </span></span><span class="ls12">x<span class="ff1 fs2 ls64 v7">1</span><span class="ff6 fs6 ls7 v0">+</span></span><span class="v0">a<span class="ff1 fs2 ls11 wse v7">22<span class="_8 blank"> </span></span><span class="ls11 ws3">x<span class="ff1 fs2 ls5f v7">2</span><span class="ff6 fs6 ls7">+</span><span class="ff7 ws2e">... <span class="ff6 fs6 ls60">+</span></span><span class="lsf">a<span class="ff1 fs2 ls65 v7">2<span class="ff5 ls62">n</span></span><span class="ls12">x<span class="fs2 ls66 v7">n</span><span class="ff6 fs6 ls9">=</span></span></span>b<span class="ff1 fs2 v7">2</span></span></span></div><div class="t m0 x32 h4 y64 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x32 h4 y65 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x32 h4 y66 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x33 h25 y67 ff5 fs1 fc1 sc0 lsd">a<span class="fs2 ls67 v7">m<span class="ff1 ls32">1</span></span><span class="ls11 ws3">x<span class="ff1 fs2 ls68 v7">1</span><span class="ff6 fs6 ls25 v0">+</span></span><span class="v0">a<span class="fs2 ls67 v7">m<span class="ff1 ls13">2</span></span><span class="ls12">x<span class="ff1 fs2 ls69 v7">2</span><span class="ff6 fs6 ls7">+</span><span class="ff7 ls11 ws2f">... <span class="ff6 fs6 ls25">+</span></span></span>a<span class="fs2 ls11 ws30 v7">m n<span class="_8 blank"> </span></span><span class="ls6a">x<span class="fs2 ls6b v7">n</span><span class="ff6 fs6 ls9">=</span><span class="ls11 ws3">b<span class="fs2 v7">m</span></span></span></span></div><div class="t m0 x7 h26 y68 ff1 fs1 fc1 sc0 ls11 ws31">de\u2026nimos a <span class="fc2 ws23 v0">matriz<span class="_d blank"> </span>de<span class="_d blank"> </span>co e\u2026cientes<span class="_d blank"> </span><span class="ff5 fc1 ls6c">A</span><span class="fc1 ws32">e a </span><span class="ws2">matriz aumentada<span class="_5 blank"> </span></span></span><span class="ff4 v11">b</span></div><div class="t m0 x34 h4 y69 ff5 fs1 fc1 sc0 ls6d">A<span class="ff1 ls11 ws3">como:</span></div><div class="t m0 x7 h27 y6a ff5 fs1 fc1 sc0 ls6e">A<span class="ff6 fs6 ls6f v0">=</span><span class="ff4 ls11 v12">2</span></div><div class="t m0 x1b h9 y6b ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x1b h9 y6c ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x1b h9 y6d ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x1b h9 y6e ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x35 hc y6f ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 ws14 v7">11<span class="_e blank"> </span></span><span class="ls70">a<span class="ff1 fs2 ls11 ws14 v7">12<span class="_f blank"> </span></span><span class="ff7 ls11 ws33">... </span></span>a<span class="ff1 fs2 ls65 v7">1<span class="ff5 ls11">n</span></span></div><div class="t m0 x35 hc y70 ff5 fs1 fc1 sc0 lsd">a<span class="ff1 fs2 ls11 ws14 v7">21<span class="_e blank"> </span></span><span class="ls70">a<span class="ff1 fs2 ls11 ws14 v7">22<span class="_f blank"> </span></span><span class="ff7 ls11 ws33">... </span></span>a<span class="ff1 fs2 ls65 v7">2<span class="ff5 ls11">n</span></span></div><div class="t m0 x36 h4 y71 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x36 h4 y72 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x36 h28 y73 ff1 fs1 fc1 sc0 ls71">.<span class="ls11 v13">.</span></div><div class="t m0 x37 h4 y72 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x37 h28 y73 ff1 fs1 fc1 sc0 ls72">.<span class="ls73 vf">.</span><span class="ls74 v14">.</span><span class="ls75 v15">.</span><span class="ls11 v13">.</span></div><div class="t m0 x1f h4 y72 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x1f h4 y73 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x38 hc y74 ff5 fs1 fc1 sc0 lsd">a<span class="fs2 ls67 v7">m<span class="ff1 ls76">1</span></span><span class="ls4">a<span class="fs2 ls67 v7">m<span class="ff1 ls77">2</span></span><span class="ff7 ls11 ws34">... </span>a<span class="fs2 ls11 ws35 v7">m n</span></span></div><div class="t m0 x39 h9 y75 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x39 h9 y76 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x39 h9 y6c ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x39 h9 y6d ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x39 h29 y6e ff4 fs1 fc1 sc0 ls78">5<span class="ff1 ls79 v4">e</span><span class="ls11 v16">b</span></div><div class="t m0 x32 h2a y77 ff5 fs1 fc1 sc0 ls7a">A<span class="ff6 fs6 ls7b v0">=</span><span class="ff4 ls11 v12">2</span></div><div class="t m0 x2e h9 y78 ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x2e h9 y79 ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x2e h9 y7a ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x2e h9 y7b ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x3a hc y7c ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 wse v7">11<span class="_e blank"> </span></span><span class="lsd">a<span class="ff1 fs2 ls11 wse v7">12<span class="_f blank"> </span></span><span class="ff7 ls11 ws36">... </span>a<span class="ff1 fs2 ls65 v7">1<span class="ff5 ls7c">n</span></span><span class="ls11 ws3">b<span class="ff1 fs2 v7">1</span></span></span></div><div class="t m0 x3a hc y7d ff5 fs1 fc1 sc0 lsf">a<span class="ff1 fs2 ls11 wse v7">21<span class="_e blank"> </span></span><span class="lsd">a<span class="ff1 fs2 ls11 wse v7">22<span class="_f blank"> </span></span><span class="ff7 ls11 ws36">... </span>a<span class="ff1 fs2 ls65 v7">2<span class="ff5 ls7c">n</span></span><span class="ls11 ws3">b<span class="ff1 fs2 v7">2</span></span></span></div><div class="t m0 x2b h4 y7e ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x2b h4 y7f ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x2b h28 y80 ff1 fs1 fc1 sc0 ls71">.<span class="ls11 v13">.</span></div><div class="t m0 x3b h4 y7f ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x3b h28 y80 ff1 fs1 fc1 sc0 ls7d">.<span class="ls74 vf">.</span><span class="ls73 v14">.</span><span class="ls7e v15">.</span><span class="ls11 v13">.</span></div><div class="t m0 x3c h4 y7f ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x3c h28 y80 ff1 fs1 fc1 sc0 ls7f">.<span class="ls11 v13">.</span></div><div class="t m0 x3d h4 y7f ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x3d h4 y80 ff1 fs1 fc1 sc0 ls11">.</div><div class="t m0 x3e hc y81 ff5 fs1 fc1 sc0 ls4">a<span class="fs2 ls67 v7">m<span class="ff1 ls80">1</span></span><span class="lsf">a<span class="fs2 ls81 v7">m<span class="ff1 ls77">2</span></span><span class="ff7 ls11 ws37">... </span></span>a<span class="fs2 ls11 ws35 v7">m n<span class="_10 blank"> </span></span><span class="ls11 ws3">b<span class="fs2 v7">m</span></span></div><div class="t m0 x3f h9 y82 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x3f h9 y78 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x3f h9 y79 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x3f h9 y7a ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x3f h9 y7b ff4 fs1 fc1 sc0 ls11">5</div><div class="t m0 x5 h5 y83 ff1 fs2 fc1 sc0 ls11">9</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg4.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y1d ff1 fs0 fc0 sc0 ls11 ws38">M<span class="_0 blank"></span>atr<span class="_0 blank"></span>iz<span class="_5 blank"> </span>Esca<span class="_0 blank"></span>lon<span class="_0 blank"></span>ad<span class="_0 blank"></span>a<span class="_2 blank"> </span>po<span class="_0 blank"></span>r<span class="_5 blank"> </span>Lin<span class="_0 blank"></span>ha<span class="_0 blank"></span>s</div><div class="t m0 x7 h4 y84 ff1 fs1 fc2 sc0 ls11 ws39">De\u2026nição: <span class="fc1 ws2">Dizemos que a linha de uma matriz tem <span class="ff5 ls82">k</span></span><span class="ws3a">zeros líderes <span class="fc1">se</span></span></div><div class="t m0 x7 h2b y85 ff1 fs1 fc1 sc0 ls11 ws24">os p<span class="_0 blank"></span>rimeiros <span class="ff5 ls83">k</span><span class="wsf">elementos da linha são to<span class="_3 blank"> </span>dos zeros e o<span class="_9 blank"> </span><span class="ff6 fs6 ls21 v0">(</span><span class="ff5 ls84 v0">k<span class="ff6 fs6 ls7">+</span><span class="ff1 ls85">1<span class="ff6 fs6 ls21 v0">)</span><span class="ls11 ws3">-ésimo</span></span></span></span></div><div class="t m0 x7 h4 y86 ff1 fs1 fc1 sc0 ls11 ws3b">elemento da linha é não-nulo.</div><div class="t m0 x7 h4 y87 ff1 fs1 fc1 sc0 ls11 wsd">Com esta terminologia, dizemos que uma matriz está em <span class="fc2 ws3">fo<span class="_0 blank"></span>rma</span></div><div class="t m0 x7 h2c y88 ff1 fs1 fc2 sc0 ls11 wsf">escalonada p<span class="_3 blank"> </span>o<span class="_0 blank"></span>r linhas <span class="fc1 ws2 v0">se cada linha tem mais zeros líderes do que a</span></div><div class="t m0 x7 h4 y89 ff1 fs1 fc1 sc0 ls11 wsf">linha p<span class="_0 blank"></span>recedente.</div><div class="t m0 x7 h4 y8a ff1 fs1 fc1 sc0 ls11 ws3c">Exemplos de matrizes escalonadas na fo<span class="_0 blank"></span>rma de linha são:</div><div class="t m0 x2 h9 y8b ff4 fs1 fc1 sc0 ls11">2</div><div class="t m0 x2 h9 y8c ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x2 h9 y8d ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x2 h9 y8e ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x29 h4 y8f ff1 fs1 fc1 sc0 ls86 ws3d">123<span class="_11 blank"></span></div><div class="t m0 x29 h4 y90 ff1 fs1 fc1 sc0 ls86 ws3d">004<span class="_11 blank"></span></div><div class="t m0 x29 h4 y91 ff1 fs1 fc1 sc0 ls86 ws3d">000<span class="_11 blank"></span></div><div class="t m0 x29 h4 y92 ff1 fs1 fc1 sc0 ls86 ws3d">000<span class="_11 blank"></span></div><div class="t m0 x23 h9 y93 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x23 h9 y94 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x23 h9 y95 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x23 h2d y96 ff4 fs1 fc1 sc0 ls87">5<span class="ff7 ls88 v17">,</span><span class="ls89 v18">\ue014</span><span class="ff1 ls8a ws3e v19">134<span class="_11 blank"></span></span></div><div class="t m0 x40 h2e y97 ff1 fs1 fc1 sc0 ls8a ws3e">016<span class="_12 blank"></span><span class="ff4 ls8b v1a">\ue015<span class="ff1 ls8c v1b">e</span><span class="ls11 vf">2</span></span></div><div class="t m0 x41 h9 y98 ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x42 h4 y99 ff1 fs1 fc1 sc0 ls11 ws3f">2 3</div><div class="t m0 x42 h4 y9a ff1 fs1 fc1 sc0 ls11 ws3f">0 6</div><div class="t m0 x42 h4 y9b ff1 fs1 fc1 sc0 ls11 ws3f">0 0</div><div class="t m0 x43 h9 y9c ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x43 h9 y98 ff4 fs1 fc1 sc0 ls11">5</div><div class="t m0 x7 h4 y9d ff1 fs1 fc1 sc0 ls11 ws2">Se uma linha da matriz escalonada p<span class="_3 blank"> </span>ossui somente zeros, então to<span class="_3 blank"> </span>das</div><div class="t m0 x7 h4 y9e ff1 fs1 fc1 sc0 ls11 wsf">as linhas subsequentes devem conter somente zeros.</div><div class="t m0 x44 h5 y9f ff1 fs2 fc1 sc0 ls11 ws14">10</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls11 ws40">M<span class="_0 blank"></span>atr<span class="_0 blank"></span>iz<span class="_5 blank"> </span>Esca<span class="_0 blank"></span>lon<span class="_0 blank"></span>ad<span class="_0 blank"></span>a<span class="_2 blank"> </span>po<span class="_0 blank"></span>r<span class="_5 blank"> </span>Lin<span class="_0 blank"></span>ha<span class="_0 blank"></span>s</div><div class="t m0 x7 h4 ya0 ff1 fs1 fc1 sc0 ls11 ws1">Uma matriz p<span class="_3 blank"> </span>o<span class="_3 blank"> </span>de ser reduzida a sua fo<span class="_0 blank"></span>rma escalonada p<span class="_3 blank"> </span>or meio das</div><div class="t m0 x7 h4 ya1 ff1 fs1 fc1 sc0 ls11 ws41">seguintes <span class="fc2 ws10 v0">op erações<span class="_d blank"> </span>elementa<span class="_0 blank"></span>res<span class="_d blank"> </span>p or<span class="_4 blank"> </span>linhas<span class="fc1">:</span></span></div><div class="t m0 x1a h1d ya2 ff5 fs4 fc0 sc0 ls27">i<span class="ff7 ls28">.<span class="ff1 fc2 ls11 ws42">P<span class="_0 blank"></span>ermutação <span class="fc1 ws6">de duas linhas de uma matriz:</span></span></span></div><div class="t m0 x22 h2f ya3 ff4 fs4 fc1 sc0 ls8d">\ue014<span class="ff1 ls11 ws43 v1c">6 3 10</span></div><div class="t m0 x45 h30 ya4 ff1 fs4 fc1 sc0 ls11 ws44">2<span class="_13 blank"> </span>1<span class="_14 blank"> </span>5 <span class="ff4 ls8e v1d">\ue015</span><span class="ff8 fs7 ws45 v5">\ue000<span class="_15 blank"></span>!</span></div><div class="t m0 x46 h31 ya5 ff1 fs2 fc1 sc0 ls11 ws46">p e r m<span class="_6 blank"> </span>ut a ç ã o<span class="_16 blank"> </span><span class="ff4 fs4 ls8f v1e">\ue014</span><span class="fs4 ws47 v1f">2 1<span class="_14 blank"> </span>5</span></div><div class="t m0 x47 h30 ya6 ff1 fs4 fc1 sc0 ls11 ws48">6<span class="_13 blank"> </span>3<span class="_13 blank"> </span>10 <span class="ff4 v1d">\ue015</span></div><div class="t m0 x1c h1d ya7 ff5 fs4 fc0 sc0 ls11 ws1e">ii <span class="ff7 ls33">.</span><span class="ff1 fc1 ws49">Alteração<span class="_4 blank"> </span>de<span class="_4 blank"> </span>uma<span class="_4 blank"> </span>linha<span class="_4 blank"> </span>pela<span class="_4 blank"> </span><span class="fc2 ws1c">adição<span class="fc1">/</span><span class="ws4a">subtração </span></span><span class="ws1d">de um múltiplo de uma</span></span></div><div class="t m0 x1b h1d ya8 ff1 fs4 fc1 sc0 ls11 ws6">outra linha:<span class="_17 blank"> </span><span class="ff4 ls90 v1c">\ue014</span><span class="ws47 v20">2 1<span class="_14 blank"> </span>5</span></div><div class="t m0 x48 h32 ya9 ff1 fs4 fc1 sc0 ls11 ws4b">6<span class="_13 blank"> </span>3<span class="_13 blank"> </span>10 <span class="ff4 ls91 v1d">\ue015</span><span class="ff8 fs7 ws45 v5">\ue000<span class="_15 blank"></span>!</span></div><div class="t m0 x49 h33 yaa ff5 fs2 fc1 sc0 ls92">L<span class="ff1 fs8 ls93 v1">2</span><span class="ff8 fsa ls94 v0">\ue000<span class="ff1 fs2 ls61">3<span class="ff5 ls95">L</span><span class="fs8 ls96 v1">1</span><span class="ff4 fs4 ls90 v21">\ue014</span><span class="fs4 ls11 ws47 v22">2 1<span class="_f blank"> </span>5</span></span></span></div><div class="t m0 x2f h32 yab ff1 fs4 fc1 sc0 ls11 ws47">0 0 <span class="ff8 fs7 ls97">\ue000</span><span class="ls98">5</span><span class="ff4 v1d">\ue015</span></div><div class="t m0 x1d h1d yac ff5 fs4 fc0 sc0 ls11 ws21">iii <span class="ff7 ls3a">.</span><span class="ff1 fc2 ws4c">Multiplicação <span class="fc1 ws1d">de cada elemento de uma linha p<span class="_3 blank"> </span>o<span class="_0 blank"></span>r uma constante não</span></span></div><div class="t m0 x1b h1d yad ff1 fs4 fc1 sc0 ls11 ws4d">nulo: <span class="ff4 ls90 v7">\ue014</span><span class="ws47 v23">2 1<span class="_f blank"> </span>5</span></div><div class="t m0 x3 h34 yae ff1 fs4 fc1 sc0 ls11 ws47">0 0 <span class="ff8 fs7 ls99">\ue000</span><span class="ls9a">5<span class="ff4 ls9b v1d">\ue015</span></span><span class="ff8 fs7 ws45 v5">\ue000<span class="_15 blank"></span>!</span></div><div class="t m0 x4a h35 yaf ff1 fs8 fc1 sc0 ls11">1</div><div class="t m0 x4a h36 yb0 ff1 fs8 fc1 sc0 ls9c">2<span class="ff5 fs2 ls9d v11">L</span><span class="ls9e v24">1</span><span class="ff4 fs4 ls8f v25">\ue014</span><span class="fs4 ls9f v26">1</span><span class="fs2 ls11 v1e">1</span></div><div class="t m0 x4b h37 yb1 ff1 fs2 fc1 sc0 lsa0">2<span class="ls11 v4">5</span></div><div class="t m0 x13 h5 yb1 ff1 fs2 fc1 sc0 ls11">2</div><div class="t m0 x3e h38 yb2 ff1 fs4 fc1 sc0 ls11 ws4e">0 0 <span class="ff8 fs7 lsa1">\ue000</span><span class="ls9a">5</span><span class="ff4 v27">\ue015</span></div><div class="t m0 x44 h5 yb3 ff1 fs2 fc1 sc0 ls11 ws14">11</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h4 yb4 ff1 fs1 fc2 sc0 ls11 ws4f">De\u2026nição: <span class="fc1 lsa2">O</span><span class="ws10">p osto<span class="_4 blank"> </span><span class="fc1 ws50">de uma<span class="_d blank"> </span>matriz é o número de linhas não-nulas em</span></span></div><div class="t m0 x7 h4 yb5 ff1 fs1 fc1 sc0 ls11 ws1">sua fo<span class="_0 blank"></span>rma escalonada p<span class="_3 blank"> </span>or linhas.</div><div class="t m0 x7 h4 yb6 ff1 fs1 fc2 sc0 ls11 ws3">Exemplos:</div><div class="t m0 x8 h39 yb7 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls11 ws51 v1">A matriz <span class="ff4 v28">2</span></span></div><div class="t m0 xc h2f yb8 ff4 fs4 fc1 sc0 ls11">6</div><div class="t m0 xc h2f yb9 ff4 fs4 fc1 sc0 ls11">6</div><div class="t m0 xc h2f yba ff4 fs4 fc1 sc0 ls11">4</div><div class="t m0 x4c h1d ybb ff1 fs4 fc1 sc0 lsa3 ws52">123<span class="_11 blank"></span></div><div class="t m0 x4c h1d ybc ff1 fs4 fc1 sc0 lsa3 ws52">004<span class="_11 blank"></span></div><div class="t m0 x4c h1d ybd ff1 fs4 fc1 sc0 lsa3 ws52">000<span class="_11 blank"></span></div><div class="t m0 x4c h1d ybe ff1 fs4 fc1 sc0 lsa3 ws52">000<span class="_11 blank"></span></div><div class="t m0 x1e h2f ybf ff4 fs4 fc1 sc0 ls11">3</div><div class="t m0 x1e h2f yc0 ff4 fs4 fc1 sc0 ls11">7</div><div class="t m0 x1e h2f yc1 ff4 fs4 fc1 sc0 ls11">7</div><div class="t m0 x1e h3a yc2 ff4 fs4 fc1 sc0 lsa4">5<span class="ff1 ls11 ws22 v14">tem<span class="_4 blank"> </span>posto<span class="_4 blank"> </span>2<span class="ff7">.</span></span></div><div class="t m0 x8 h3b yc3 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls11 ws51 v1">A matriz <span class="ff4 ls90 v29">\ue014</span><span class="ws53 v2a">6 3 10</span></span></div><div class="t m0 x4d h34 yc4 ff1 fs4 fc1 sc0 ls11 ws54">2<span class="_13 blank"> </span>1<span class="_14 blank"> </span>5 <span class="ff4 lsa5 v1d">\ue015</span><span class="ws1d v5">tem p<span class="_3 blank"> </span>osto 2 (vide slide anterio<span class="_0 blank"></span>r).</span></div><div class="t m0 x8 h3c yc5 ff2 fs3 fc0 sc0 ls0">I<span class="ff1 fs4 fc1 ls11 ws51 v1">A matriz <span class="ff4 ls90 v29">\ue014</span><span class="ws53 v2a">6 3</span></span></div><div class="t m0 x4d h34 yc6 ff1 fs4 fc1 sc0 ls11 ws55">2<span class="_13 blank"> </span>1 <span class="ff4 lsa6 v1d">\ue015</span><span class="ws22 v5">tem<span class="_4 blank"> </span>posto<span class="_4 blank"> </span>1.</span></div><div class="t m0 x44 h5 yc7 ff1 fs2 fc1 sc0 ls11 ws14">12</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg5.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y1d ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h4 yc8 ff1 fs1 fc1 sc0 ls11 ws56">Dada uma matriz <span class="ff5 ls6c">A</span><span class="ws57">com <span class="fc2 lsa7">n</span><span class="ws58">linhas e <span class="fc2 lsa8">m</span><span class="ws3">colunas:</span></span></span></div><div class="t m0 x0 h3d yc9 ff5 fs1 fc1 sc0 ls11 ws59">p osto<span class="_5 blank"> </span>A<span class="_13 blank"> </span><span class="ff8 fs6 lsa9 v0">\ue014</span><span class="lsaa v0">n<span class="fs2 lsab va">o</span><span class="ff1 ls11 ws5a">linhas de <span class="ff5">A</span></span></span></div><div class="t m0 x4e h3e yca ff8 fs6 fc1 sc0 lsa9">\ue014<span class="ff5 fs1 lsaa">n<span class="fs2 lsab va">o</span><span class="ff1 ls11 ws2">colunas de <span class="ff5">A</span></span></span></div><div class="t m0 x7 h3f ycb ff1 fs1 fc1 sc0 ls11 ws5b">i.e. <span class="ff5 ws10">p osto<span class="_5 blank"> </span>A<span class="_a blank"> </span><span class="ff8 fs6 ls9 v0">\ue014</span></span><span class="ws5c v0">min <span class="ff8 fs6 lsac v0">f</span><span class="ff5 lsaa">n<span class="ff7 lsad">,</span><span class="lsae">m<span class="ff8 fs6 lsaf v0">g</span></span></span><span class="ff7">.</span></span></div><div class="t m0 x7 h4 ycc ff1 fs1 fc1 sc0 ls11 wsd">Intuitivamente, o p<span class="_3 blank"> </span>osto de <span class="ff5 ls6c">A</span><span class="ws3c">é limitado p<span class="_3 blank"> </span>ele número de suas <span class="fc2 ws3">entradas</span></span></div><div class="t m0 x7 h4 ycd ff1 fs1 fc2 sc0 ls11 ws3">diagonais<span class="fc1 v0">.</span></div><div class="t m0 x44 h5 yce ff1 fs2 fc1 sc0 ls11 ws14">13</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h11 ycf ff1 fs1 fc1 sc0 ls11 ws5d">P<span class="_0 blank"></span>or exemplo, considere uma matriz <span class="ff5 lsb0">B</span><span class="ws5e">de<span class="_4 blank"> </span>tamanho<span class="_d blank"> </span>3 <span class="ff8 fs6 ls7">\ue002</span><span class="wsd">5 e uma</span></span></div><div class="t m0 x7 h40 yd0 ff1 fs1 fc1 sc0 ls11 ws5f">matriz <span class="ff5 lsb1">C</span><span class="ws60">de<span class="_d blank"> </span>tamanho<span class="_d blank"> </span>4 <span class="ff8 fs6 ls7 v0">\ue002</span><span class="wsf v0">2.<span class="_2 blank"> </span>O "<span class="fc2 ws59">p osto<span class="_d blank"> </span>máximo</span><span class="ws61">" dessas matrizes é:</span></span></span></div><div class="t m0 x4f h41 yd1 ff5 fs1 fc1 sc0 ls11 ws10">p osto<span class="_5 blank"> </span>B<span class="_9 blank"> </span><span class="ff8 fs6 ls9 v0">\ue014</span><span class="v0">p osto<span class="_1 blank"> </span><span class="ff4 v1a">2</span></span></div><div class="t m0 x48 h9 yd2 ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x16 h11 yd3 ff8 fs6 fc1 sc0 ls11 ws62">\ue003 \ue003 \ue003 \ue003 \ue003</div><div class="t m0 x16 h11 yd4 ff1 fs1 fc1 sc0 lsb2">0<span class="ff8 fs6 ls11 ws62">\ue003 \ue003 \ue003 \ue003</span></div><div class="t m0 x16 h11 yd5 ff1 fs1 fc1 sc0 ls11 ws63">0 0 <span class="ff8 fs6 ws62">\ue003 \ue003 \ue003</span></div><div class="t m0 x2e h9 yd6 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x2e h9 yd7 ff4 fs1 fc1 sc0 lsb3">5<span class="ff6 fs6 ls9 v2b">=</span><span class="ff1 ls11 ws64 v2b">3<span class="_d blank"> </span>( <span class="ff6 fs6 ls3b">=<span class="ff5 fs1 lsb4">n<span class="fs2 lsab va">o</span></span></span><span class="ws65">linhas de <span class="ff5 lsb5">B</span>)</span></span></div><div class="t m0 x7 h4 yd8 ff1 fs1 fc1 sc0 ls11">e</div><div class="t m0 x50 h42 yd9 ff5 fs1 fc1 sc0 ls11 ws10">p osto<span class="_5 blank"> </span>C<span class="_5 blank"> </span><span class="ff8 fs6 ls9 v0">\ue014</span><span class="ws11 v0">p osto<span class="_1 blank"> </span><span class="ff4 v2c">2</span></span></div><div class="t m0 x1f h9 yda ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x1f h9 ydb ff4 fs1 fc1 sc0 ls11">6</div><div class="t m0 x1f h9 ydc ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x25 h11 ydd ff8 fs6 fc1 sc0 ls11 ws62">\ue003 \ue003</div><div class="t m0 x25 h11 yde ff1 fs1 fc1 sc0 lsb2">0<span class="ff8 fs6 ls11">\ue003</span></div><div class="t m0 x25 h4 ydf ff1 fs1 fc1 sc0 ls11 ws66">0 0</div><div class="t m0 x25 h4 ye0 ff1 fs1 fc1 sc0 ls11 ws66">0 0</div><div class="t m0 x2c h9 ye1 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x2c h9 ye2 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x2c h9 ye3 ff4 fs1 fc1 sc0 ls11">7</div><div class="t m0 x2c h43 ye4 ff4 fs1 fc1 sc0 lsb6">5<span class="ff6 fs6 ls3b v17">=</span><span class="ff1 ls11 ws64 v17">2<span class="_d blank"> </span>( <span class="ff6 fs6 ls9">=<span class="ff5 fs1 lsb7">n<span class="fs2 lsab va">o</span></span></span><span class="wsf">colunas de <span class="ff5 lsb8">C</span>)</span></span></div><div class="t m0 x44 h5 ye5 ff1 fs2 fc1 sc0 ls11 ws14">14</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h4 ye6 ff1 fs1 fc2 sc0 ls11 wsd">Exemplo 1:<span class="_2 blank"> </span><span class="fc1 ws2">Lemb<span class="_0 blank"></span>re-se que, na aula passada, vimos que o sistema:</span></div><div class="t m0 xb h9 ye7 ff4 fs1 fc1 sc0 lsb9">\ue01a<span class="ff5 ls12 v2">x</span><span class="ff1 fs2 lsba v3">1</span><span class="ff8 fs6 ls25 v2">\ue000</span><span class="ff1 ls11 ws3 v2">2<span class="ff5">x<span class="ff1 fs2 lsbb v7">2</span><span class="ff6 fs6 ls9">=</span><span class="ff1">8</span></span></span></div><div class="t m0 x39 h40 ye8 ff1 fs1 fc1 sc0 ls11 ws3">3<span class="ff5">x</span><span class="fs2 lsbc v7">1</span><span class="ff6 fs6 ls25 v0">+</span><span class="ff5 v0">x</span><span class="fs2 lsbd v7">2</span><span class="ff6 fs6 ls9 v0">=</span><span class="v0">3</span></div><div class="t m0 x7 h40 ye9 ff1 fs1 fc1 sc0 ls11 ws10">p ossui<span class="_d blank"> </span>uma<span class="_d blank"> </span><span class="fc2 ws1 v0">única solução<span class="fc1 lse">,<span class="ff5 ls12">x</span><span class="fs2 lsbe v7">1</span><span class="ff6 fs6 ls9">=</span><span class="ls11 ws2">2 e <span class="ff5 ls12">x</span><span class="fs2 lsbf v7">2</span><span class="ff6 fs6 ls7b">=<span class="ff8 lsc0">\ue000</span></span><span class="ws3">3<span class="ff7">.</span></span></span></span></span></div><div class="t m0 x7 h4 yea ff1 fs1 fc1 sc0 ls11 wsd">Note que, neste caso, escalonando as matrizes de co<span class="_3 blank"> </span>e\u2026cientes e</div><div class="t m0 x7 h4 yeb ff1 fs1 fc1 sc0 ls11 wsd">aumentada, obtemos:</div><div class="t m0 x51 h44 yec ff5 fs1 fc1 sc0 lsc1">A<span class="ff6 fs6 ls6f v0">=</span><span class="ff4 lsc2 v6">\ue014</span><span class="ff1 lsc3 vf">1</span><span class="ff8 fs6 lsc0 vf">\ue000</span><span class="ff1 ls11 vf">2</span></div><div class="t m0 x23 h45 yed ff1 fs1 fc1 sc0 ls11 ws67">3<span class="_18 blank"> </span>1 <span class="ff4 lsc4 v1a">\ue015</span><span class="ff6 fsb lsc5 v29">(</span><span class="ff9 fs2 ws68 v29">...</span><span class="ff6 fsb v29">)</span></div><div class="t m0 x32 h46 yee ff8 fs6 fc1 sc0 ls11 ws69">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 lsc6 v6">\ue014<span class="ff1 lsc7 v2">1</span></span><span class="lsc0 vf">\ue000</span><span class="ff1 fs1 vf">2</span></div><div class="t m0 x2f h45 yed ff1 fs1 fc1 sc0 ls11 ws67">0<span class="_18 blank"> </span>7 <span class="ff4 v1a">\ue015</span></div><div class="t m0 x7 h4 yef ff1 fs1 fc1 sc0 ls11">e</div><div class="t m0 x2 h9 yf0 ff4 fs1 fc1 sc0 ls11">b</div><div class="t m0 x52 h47 yf1 ff5 fs1 fc1 sc0 lsc8">A<span class="ff6 fs6 ls7b v0">=</span><span class="ff4 ls89 v6">\ue014</span><span class="ff1 lsc3 vf">1</span><span class="ff8 fs6 lsc0 vf">\ue000</span><span class="ff1 ls11 ws3f vf">2 8</span></div><div class="t m0 x0 h48 yf2 ff1 fs1 fc1 sc0 ls11 ws6a">3<span class="_18 blank"> </span>1<span class="_18 blank"> </span>3 <span class="ff4 lsc4 v1a">\ue015</span><span class="ff6 fsb lsc9 v29">(</span><span class="ff9 fs2 ws6b v29">...</span><span class="ff6 fsb v29">)</span></div><div class="t m0 x10 h49 yf3 ff8 fs6 fc1 sc0 ls11 ws6c">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 lsc6 v6">\ue014<span class="ff1 lsca v2">1</span></span><span class="lsc0 vf">\ue000</span><span class="ff1 fs1 ws6d vf">2 8</span></div><div class="t m0 x53 h48 yf2 ff1 fs1 fc1 sc0 ls11 ws6e">0 7 <span class="ff8 fs6 lscb">\ue000</span><span class="ws6f">21 <span class="ff4 v1a">\ue015</span></span></div><div class="t m0 x7 h4a yf4 ff1 fs1 fc1 sc0 ls11 ws70">P<span class="_0 blank"></span>ortanto, <span class="ff5 ws10">posto<span class="_5 blank"> </span>A<span class="_4 blank"> </span><span class="ff6 fs6 ls9 v0">=</span><span class="ws59 v0">posto<span class="_b blank"> </span><span class="ff4 v11">b</span></span></span></div><div class="t m0 x17 h4b yf5 ff5 fs1 fc1 sc0 lscc">A<span class="ff6 fs6 ls9">=</span><span class="ff1 ls11 ws71">2<span class="_d blank"> </span>(<span class="ff6 fs6 ls3b">=</span></span><span class="lscd">n<span class="fs2 lsce v14">o</span><span class="ls11 ws72">vari <span class="ffa ws73">´<span class="_12 blank"></span><span class="ff5 ws74">a veis<span class="_8 blank"> </span><span class="ff1 ws3">)<span class="ff7">.</span></span></span></span></span></span></div><div class="t m0 x44 h5 y1c ff1 fs2 fc1 sc0 ls11 ws14">15</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/142c4146-a316-4f73-87e9-9c505cdf8156/bg6.png"><div class="c x0 y1 w2 h2"><div class="t m0 x6 h3 y1d ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h4 yf6 ff1 fs1 fc2 sc0 ls11 wsd">Exemplo 2:<span class="_2 blank"> </span><span class="fc1 wsf">O sistema:</span></div><div class="t m0 xa h9 yf7 ff4 fs1 fc1 sc0 lsb9">\ue01a<span class="ff5 ls11 ws3 v2">x</span><span class="ff1 fs2 lscf v3">1</span><span class="ff6 fs6 ls25 v2">+</span><span class="ff1 ls11 ws3 v2">2<span class="ff5">x<span class="ff1 fs2 lsd0 v7">2</span><span class="ff6 fs6 ls7">+</span></span>3<span class="ff5">x</span><span class="fs2 lsd1 v7">3</span><span class="ff6 fs6 ls3b">=</span>1</span></div><div class="t m0 xb h40 yf8 ff1 fs1 fc1 sc0 ls11 ws3">3<span class="ff5">x</span><span class="fs2 lsd2 v7">1</span><span class="ff6 fs6 ls25 v0">+</span><span class="v0">2<span class="ff5">x</span><span class="fs2 lsd0 v7">2</span><span class="ff6 fs6 ls25">+</span><span class="ff5">x</span><span class="fs2 lsbd v7">3</span><span class="ff6 fs6 ls3b">=</span>1</span></div><div class="t m0 x7 h4c yf9 ff1 fs1 fc1 sc0 ls11 ws10">p ossui<span class="_d blank"> </span><span class="fc2 ws75 v0">in\u2026nitas soluções <span class="fc1 ws76">dadas<span class="_d blank"> </span>p o<span class="_0 blank"></span>r:<span class="_2 blank"> </span><span class="ff5 ws3">x</span><span class="fs2 lsd3 v7">1</span><span class="ff6 fs6 ls9">=</span><span class="ff5 ls12">x</span><span class="fs2 lsd4 v7">3</span><span class="lsd5">e<span class="ff5 ls12">x</span><span class="fs2 lsd6 v7">2</span><span class="ff6 fs6 lsd7">=</span></span><span class="ws3">0<span class="ff7 lsad">,</span><span class="lsd8">5<span class="ff8 fs6 ls7">\ue000</span></span>2<span class="ff5 ls12">x</span><span class="fs2 lsd9 v7">3</span><span class="ff7">.</span></span></span></span></div><div class="t m0 x7 h4 yfa ff1 fs1 fc1 sc0 ls11 wsd">Note que, neste caso, escalonando as matrizes de co<span class="_3 blank"> </span>e\u2026cientes e</div><div class="t m0 x7 h4 yfb ff1 fs1 fc1 sc0 ls11 wsd">aumentada, obtemos:</div><div class="t m0 xc h4d yfc ff5 fs1 fc1 sc0 lsc1">A<span class="ff6 fs6 ls7b v0">=</span><span class="ff4 ls89 v6">\ue014</span><span class="ff1 ls8a ws3e vf">123<span class="_11 blank"></span></span></div><div class="t m0 x48 h4e yfd ff1 fs1 fc1 sc0 ls8a ws3e">321<span class="_12 blank"></span><span class="ff4 lsc4 v1a">\ue015<span class="ff6 fsb lsc5 v1c">(<span class="ff9 fs2 ls11 ws68 v0">...</span><span class="ls11">)</span></span></span></div><div class="t m0 x54 h46 yfe ff8 fs6 fc1 sc0 ls11 ws77">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 lsc6 v6">\ue014</span><span class="ff1 fs1 ws6e vf">1 2<span class="_19 blank"> </span>3</span></div><div class="t m0 x55 h4f yfd ff1 fs1 fc1 sc0 lsca">0<span class="ff8 fs6 lsc0 v0">\ue000</span><span class="lsda v0">4<span class="ff8 fs6 lsc0">\ue000</span><span class="lsdb">8<span class="ff4 ls11 v1a">\ue015</span></span></span></div><div class="t m0 x7 h4 yff ff1 fs1 fc1 sc0 ls11">e</div><div class="t m0 x27 h9 y100 ff4 fs1 fc1 sc0 ls11">b</div><div class="t m0 x27 h50 y101 ff5 fs1 fc1 sc0 lsdc">A<span class="ff6 fs6 ls7b v0">=</span><span class="ff4 lsc2 v6">\ue014</span><span class="ff1 ls11 ws3f vf">1 2 3 1</span></div><div class="t m0 x56 h48 y102 ff1 fs1 fc1 sc0 ls11 ws3f">3 2 1 1<span class="_b blank"> </span><span class="ff4 lsdd v1a">\ue015</span><span class="ff6 fsb lsc9 v29">(</span><span class="ff9 fs2 ws6b v29">...</span><span class="ff6 fsb v29">)</span></div><div class="t m0 x57 h46 y103 ff8 fs6 fc1 sc0 ls11 ws6c">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 lsde v6">\ue014</span><span class="ff1 fs1 ws78 vf">1<span class="_18 blank"> </span>2 3 1</span></div><div class="t m0 x58 h51 y102 ff1 fs1 fc1 sc0 lsdf">0<span class="ff8 fs6 lscb v0">\ue000</span><span class="lse0 v0">4<span class="ff8 fs6 lscb">\ue000</span><span class="lse1">8<span class="ff8 fs6 lsc0">\ue000</span><span class="lse2">2<span class="ff4 ls11 v1a">\ue015</span></span></span></span></div><div class="t m0 x7 h52 y104 ff1 fs1 fc1 sc0 ls11 ws70">P<span class="_0 blank"></span>ortanto, <span class="ff5 ws10">posto<span class="_5 blank"> </span>A<span class="_4 blank"> </span><span class="ff6 fs6 ls9 v0">=</span><span class="ws59 v0">posto<span class="_b blank"> </span><span class="ff4 v11">b</span></span></span></div><div class="t m0 x17 h4b y105 ff5 fs1 fc1 sc0 lscc">A<span class="ff6 fs6 ls9">=</span><span class="ff1 ls11 ws71">2<span class="_d blank"> </span>(<span class="ffb fs6 ls9"><</span></span><span class="lse3">n<span class="fs2 lsce v14">o</span><span class="ls11 ws79">vari <span class="ffa ws73">´<span class="_12 blank"></span><span class="ff5 ws7a">a veis<span class="_8 blank"> </span><span class="ff1 wsd">), i.e.<span class="_2 blank"> </span>dizemos que</span></span></span></span></span></div><div class="t m0 x7 h4 y106 ff1 fs1 fc1 sc0 ls11 ws1">existe uma "<span class="fc2 ws56 v0">va<span class="_0 blank"></span>riável livre<span class="fc1 ws2">" neste sistema.</span></span></div><div class="t m0 x44 h5 yce ff1 fs2 fc1 sc0 ls11 ws14">16</div></div><div class="c x0 y7 w2 h2"><div class="t m0 x6 h3 y8 ff1 fs0 fc0 sc0 ls11 ws4">P<span class="_7 blank"></span>osto</div><div class="t m0 x7 h4 y107 ff1 fs1 fc2 sc0 ls11 wsd">Exemplo 3:<span class="_2 blank"> </span><span class="fc1 wsf">O sistema:<span class="_1a blank"> </span><span class="ff4 v2">8</span></span></div><div class="t m0 x59 h9 y108 ff4 fs1 fc1 sc0 ls11"><</div><div class="t m0 x59 h9 y109 ff4 fs1 fc1 sc0 ls11">:</div><div class="t m0 x5a h53 y10a ff5 fs1 fc1 sc0 ls11 ws3">x<span class="ff1 fs2 lse4 v7">1</span><span class="ff6 fs6 ls7 v0">+</span><span class="ff1 v0">3<span class="ff5 ls12">x</span><span class="fs2 lse5 v7">2</span><span class="ff6 fs6 ls9">=</span>1</span></div><div class="t m0 x5a h40 y10b ff1 fs1 fc1 sc0 ls11 ws3">3<span class="ff5">x</span><span class="fs2 lse6 v7">1</span><span class="ff6 fs6 ls7 v0">+<span class="ff5 fs1 ls12">x</span></span><span class="fs2 ls19 v7">2</span><span class="ff6 fs6 ls9 v0">=</span><span class="v0">1</span></div><div class="t m0 x20 h40 y10c ff1 fs1 fc1 sc0 ls11 ws3">2<span class="ff5">x</span><span class="fs2 lse7 v7">1</span><span class="ff6 fs6 ls60 v0">+</span><span class="v0">3<span class="ff5 ls5">x</span><span class="fs2 lse8 v7">2</span><span class="ff6 fs6 ls3b">=</span>1</span></div><div class="t m0 x7 h4 y10d ff1 fs1 fc1 sc0 ls11 ws10">p ossui<span class="_d blank"> </span><span class="fc2 wsf v0">nenhuma solução<span class="fc1">.</span></span></div><div class="t m0 x7 h4 y10e ff1 fs1 fc1 sc0 ls11 ws3c">Note que, neste caso, escalonando as matrizes de co<span class="_3 blank"> </span>e\u2026cientes e</div><div class="t m0 x7 h4 y10f ff1 fs1 fc1 sc0 ls11 wsd">aumentada, obtemos:</div><div class="t m0 x5b h54 y110 ff5 fs1 fc1 sc0 lse9">A<span class="ff6 fs6 ls6f v0">=</span><span class="ff4 ls11 v1a">2</span></div><div class="t m0 xe h9 y111 ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x1e h4 y112 ff1 fs1 fc1 sc0 ls11 ws7b">1 3</div><div class="t m0 x1e h4 y113 ff1 fs1 fc1 sc0 ls11 ws7b">3 2</div><div class="t m0 x1e h4 y114 ff1 fs1 fc1 sc0 ls11 ws7b">2 3</div><div class="t m0 x24 h9 y115 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x24 h55 y111 ff4 fs1 fc1 sc0 lsea">5<span class="ff6 fsb lsc5 v10">(</span><span class="ff9 fs2 ls11 ws6b v2d">...<span class="ff6 fsb v0">)</span></span></div><div class="t m0 x2c h56 y116 ff8 fs6 fc1 sc0 ls11 ws77">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 v1a">2</span></div><div class="t m0 x2e h9 y111 ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x3e h4 y112 ff1 fs1 fc1 sc0 ls11 ws6e">1 3</div><div class="t m0 x3e h57 y113 ff1 fs1 fc1 sc0 lsc7">0<span class="ff8 fs6 lsc0 v0">\ue000</span><span class="ls11 v0">8</span></div><div class="t m0 x3e h4 y117 ff1 fs1 fc1 sc0 ls11 ws6e">0 0</div><div class="t m0 x13 h9 y118 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x13 h9 y119 ff4 fs1 fc1 sc0 ls11">5</div><div class="t m0 x7 h4 y11a ff1 fs1 fc1 sc0 ls11">e</div><div class="t m0 x5c h9 y11b ff4 fs1 fc1 sc0 ls11">b</div><div class="t m0 x5c h58 y11c ff5 fs1 fc1 sc0 lseb">A<span class="ff6 fs6 ls6f v0">=</span><span class="ff4 ls11 v1a">2</span></div><div class="t m0 x22 h9 y11d ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x5d h4 y11e ff1 fs1 fc1 sc0 ls8a ws3e">131<span class="_11 blank"></span></div><div class="t m0 x5d h4 y11f ff1 fs1 fc1 sc0 ls8a ws3e">321<span class="_11 blank"></span></div><div class="t m0 x5d h4 y120 ff1 fs1 fc1 sc0 ls8a ws3e">231<span class="_11 blank"></span></div><div class="t m0 x4e h9 y121 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x4e h59 y122 ff4 fs1 fc1 sc0 lsec">5<span class="ff6 fsb lsed v10">(</span><span class="ff9 fs2 ls11 ws6b v2d">...<span class="ff6 fsb v0">)</span></span></div><div class="t m0 x54 h56 y123 ff8 fs6 fc1 sc0 ls11 ws77">\ue000<span class="_15 blank"></span>! <span class="ff4 fs1 v1a">2</span></div><div class="t m0 x5e h9 y11d ff4 fs1 fc1 sc0 ls11">4</div><div class="t m0 x55 h4 y124 ff1 fs1 fc1 sc0 ls11 ws6e">1 3<span class="_1b blank"> </span>1</div><div class="t m0 x55 h5a y125 ff1 fs1 fc1 sc0 lsca">0<span class="ff8 fs6 lsee v0">\ue000</span><span class="lsef v0">8<span class="ff8 fs6 lsc0">\ue000</span><span class="ls11">2</span></span></div><div class="t m0 x55 h5b y126 ff1 fs1 fc1 sc0 ls11 ws6e">0 0 <span class="ff8 fs6 lsf0 v0">\ue000</span><span class="fs2 v17">1</span></div><div class="t m0 x5f h5 y127 ff1 fs2 fc1 sc0 ls11">4</div><div class="t m0 x60 h9 y128 ff4 fs1 fc1 sc0 ls11">3</div><div class="t m0 x60 h9 y129 ff4 fs1 fc1 sc0 ls11">5</div><div class="t m0 x7 h5c y12a ff1 fs1 fc1 sc0 ls11 ws7c">P<span class="_0 blank"></span>ortanto, <span class="ff5 ws10">posto<span class="_5 blank"> </span>A<span class="_4 blank"> </span><span class="ff6 fs6 ls9">=</span></span><span class="lsf1">2<span class="ffb fs6 ls9"><</span></span><span class="ff5 ws59">posto<span class="_b blank"> </span><span class="ff4 v11">b</span></span></div><div class="t m0 x57 h4 y12a ff5 fs1 fc1 sc0 ls11 ws3">A<span class="ff1">.</span></div><div class="t m0 x44 h5 y12b ff1 fs2 fc1 sc0 ls11 ws14">17</div></div><div class="c x0 y14 w2 h2"><div class="t m0 x6 h3 y15 ff1 fs0 fc0 sc0 ls11 ws7d">P<span class="_7 blank"></span>osto<span class="_0 blank"></span>:<span class="_1 blank"> </span>T<span class="_15 blank"></span>eo<span class="_0 blank"></span>rem<span class="_0 blank"></span>a<span class="_5 blank"> </span>de<span class="_5 blank"> </span>Ro<span class="_0 blank"></span>uch<span class="_0 blank"></span>é-C<span class="_0 blank"></span>apelli</div><div class="t m0 x7 h4 y12c ff1 fs1 fc2 sc0 ls11 ws7e">T<span class="_c blank"></span>eorema: <span class="fc1 wsd">Dado um sistema de <span class="ff5 lsf2">m</span><span class="ws7f">equações linea<span class="_0 blank"></span>res e <span class="ff5 lsf3">n</span><span class="ws3">variáveis,</span></span></span></div><div class="t m0 x7 h4 y12d ff1 fs1 fc1 sc0 ls11 wsf">temos que:</div><div class="t m0 x1c h5d y12e ff1 fs4 fc0 sc0 ls11 ws1c">1<span class="ff7 lsf4">.</span><span class="fc1 ws22">Se<span class="_4 blank"> </span>posto<span class="_4 blank"> </span><span class="ff5 lsf5">A<span class="ff6 fs7 lsf6">=</span></span>p osto<span class="_9 blank"> </span><span class="ff4 v11">b</span></span></div><div class="t m0 x16 h1d y12e ff5 fs4 fc1 sc0 ls11 ws1c">A<span class="ff1 ws1d">, então o sistema admite solução.</span></div><div class="t m0 x61 h5e y12f ff1 fs5 fc0 sc0 lsf7">1<span class="ff3 lsf8">.</span><span class="lsf9">1<span class="fc1 ls11 ws80">Se<span class="_4 blank"> </span>p<span class="_3 blank"> </span>os t o<span class="_4 blank"> </span><span class="ff5 lsfa">A<span class="ff6 fsc lsfb">=</span></span>p<span class="_3 blank"> </span>o s t o<span class="_9 blank"> </span><span class="ff4 v2e">b</span></span></span></div><div class="t m0 x62 h5f y12f ff5 fs5 fc1 sc0 lsfc">A<span class="ff6 fsc lsfb">=</span><span class="lsfd">n<span class="ff1 ls11 ws9">,<span class="_a blank"> </span>e n t ã o<span class="_4 blank"> </span>exi s te<span class="_4 blank"> </span>um<span class="_3 blank"> </span>a<span class="_4 blank"> </span>úni c a<span class="_4 blank"> </span>sol u ç ã o<span class="_4 blank"> </span>(i.e .<span class="_5 blank"> </span>o</span></span></div><div class="t m0 x27 h7 y130 ff1 fs5 fc1 sc0 ls11 ws81">sist e<span class="_3 blank"> </span>m a<span class="_4 blank"> </span>é<span class="_4 blank"> </span>po<span class="_3 blank"> </span>ss ív e<span class="_3 blank"> </span>l<span class="_4 blank"> </span>e<span class="_a blank"> </span>de t e r m<span class="_3 blank"> </span>in a d<span class="_3 blank"> </span>o) .</div><div class="t m0 x61 h60 y131 ff1 fs5 fc0 sc0 lsf7">1<span class="ff3 lsf8">.</span><span class="lsf9">2<span class="fc1 ls11 ws80">Se<span class="_4 blank"> </span>p<span class="_3 blank"> </span>os t o<span class="_4 blank"> </span><span class="ff5 lsfa">A<span class="ff6 fsc lsfb">=</span></span>p<span class="_3 blank"> </span>o s t o<span class="_9 blank"> </span><span class="ff4 v2e">b</span></span></span></div><div class="t m0 x62 h7 y131 ff5 fs5 fc1 sc0 lsfc">A<span class="ffb fsc lsfb"><</span><span class="lsfd">n<span class="ff1 ls11 ws9">,<span class="_a blank"> </span>e n t ã o<span class="_4 blank"> </span>exi s te m<span class="_4 blank"> </span>in \u2026 n i t a s<span class="_4 blank"> </span>sol u ç õ e s<span class="_4 blank"> </span>(i.e .<span class="_5 blank"> </span>o</span></span></div><div class="t m0 x27 h7 y132 ff1 fs5 fc1 sc0 ls11 ws81">sist e<span class="_3 blank"> </span>m a<span class="_4 blank"> </span>é<span class="_4 blank"> </span>po<span class="_3 blank"> </span>ss ív e<span class="_3 blank"> </span>l<span class="_4 blank"> </span>e<span class="_a blank"> </span>in d e t e r m<span class="_3 blank"> </span>in a d o<span class="_3 blank"> </span>).</div><div class="t m0 x1c h61 y133 ff1 fs4 fc0 sc0 ls11 ws1c">2<span class="ff7 lsf4">.</span><span class="fc1 ws22">Se<span class="_4 blank"> </span>posto<span class="_4 blank"> </span><span class="ff5 lsf5">A<span class="ffb fs7 lsf6"><</span></span>p osto<span class="_9 blank"> </span><span class="ff4 v11">b</span></span></div><div class="t m0 x16 h1d y133 ff5 fs4 fc1 sc0 ls11 ws1c">A<span class="ff1 ws1d">, então o sistema não admite solução (i.e.<span class="_5 blank"> </span>o</span></div><div class="t m0 x1b h1d y134 ff1 fs4 fc1 sc0 ls11 ws22">sistema<span class="_4 blank"> </span>é<span class="_4 blank"> </span>impossível).</div><div class="t m0 x44 h5 y1c ff1 fs2 fc1 sc0 ls11 ws14">18</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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