Buscar

Álgebra Linear I - Poli - Resumo P2 Arthur Salles

Prévia do material em texto

-
''RE5U f\f\O de ALG-tLf NT 'VOf\d CÂ ~2
-----------------~--------------------~
. trfl oo.!.- iY1r~~ 5I>bu aulo. clt I11vi~ vtl FhWK ) ~ { AlJ~o$rh U~tlI~J
9!Y1 ; AJ hUn So-rjjeS 1 EXERC íc. (as sU(l.ER llXlS JJE ffl71h1 .
I - 1<1v t5ãe (~ ~ae to.B 1\ JtG- /I ~-- )
~ .'
'RLv~'" 1'11> fUNlIll1/} ch fiJ as 16pícll5 ; Ve-k-un (Dei", ~-b .tD~ )
ALúm diSSiI J rntÇííe Mtj!fl\al cyu ~ ~ rn&\(O. ~<l: JJ>j{ .u
j)(?Qt'CAd~·
J[- 'Bo.bl ~ ~ ~ ~
~
j) Úrrf\b1(\Q~ lLr1JN,--
V t10'\U) I JiJ())lfl)OJ
tcü~ '1),1.1. '.
; ~ &5 ~JJl JJI'fl Vl-J.... :t:. i tlYrrJ lu Y'Il~ ltVUlJ/\ di att-ltirv
y 1 Uí I se- e S&mlm-k se lXiS tl/rf) tI(..l '{> € IR
-I -+ -I
U ::; o(v + 'P lJJ
Nl).. ptlLÍtlCA I d().~: ~ ~ (X.I I v( ,-:{( J ,V ~ (Kl Yt 1Z) .... (' )L; . I J '. 'J Á III z: X3, '(5,35
!:2l~J!JJurmàJ S~ 9 \ M.l ~ U I V IÚJ ~ 1 I rntmkmb ty dli~() ()jr,li
~ GlII m \1UOlTIlll ~ I eo.ch v.t~ .\Jlfl JJJlfQ kl~.
Ntt e-C>&1) rM. f ~ (1 I w f : U7 / ~( y( 3 i GJuJ".., l(t. Y! 3! .J CYl1)8Q
W" )(-5 y3 3~
5..n- f z: O : CfJ PLAAJARtt;
> O ',: 'BASE 1'Obl f"IVA
-: O : 1lGt. I\fEJrkTWA
1li - 1If1ê d,u-b V t~J
~ ---~~~F~ )Il'lW d~ v; ~ _5111',h6~t)oJ. pll'l A . ('Ps1 J.kJJrtJf~b ; U liV i
e ~cJ,Ae V.l-WU<J. Ji1111'l \) 1..v )
~ >wc .JUJ>Uli<x~,[ lJJlY\ Irlh1 {Ob (ffi'Iil\ÓJlie ~ ~ JDcJtIIIl q,w c/;C !J(TfI ~ )
__F,,~ ch 1'1~ C ~'0 \'nêlLJe l'l'Il'l t1~ cl;1\l~ À. l>N'1tiJ!J u x v
I1 ~ 1\ ç: fi : 11 C ~ ~~ 1\ .hJ!nev i u
~ = (XI I yl (~/I
J J;: I«1 I yt I)l I
..". -1
li "v " (~ 1".dom JJrtIi I ~1l<.d""J ..\irtI ~ ,11ki;n)
@-
-
~ J 2~ I
-{ 2> 4
.;. .~
~ -Zj +3t -fel
:: ( _ ~ J -G /3)-t> .."
.'. Uf\V
..L
&. Ilv j :C J ( ha,1I z: rz
.~ l;umdê- 'J..U
-,
, j:.(thJ1 ~cfo G-~-tIlJ:CA ....
1\iJ " V 1I re<ll ..wJl v iSt" (Wfl8 ~ lÀti.ttI :J - -- -
do- potl<l1Í qr <4iwn'l1I1lch pe1 t J. V L~~ ÁtJJ>. ~ I ijA j; II
U
~b5 tJ & ~JJl ~ e.JuJM ~ MIa rit ~rtl wóinOf-Q.a- AU I ~ ~
J,Je:,.. (i/f, ~ iL ) ~ v lfl'rl&i iJl,l; D(
.A-- 7 A WA A~ '" ~~ ~ fJiJIl cft y-L1~a
~/ A+' z: IlM/I'kll-/ u .
A j) . Z
~b5 2) :LS~ f~<P. },.\}\ IJ~Je foro.-. cV..'bJ1Jlf1l l'1!>11 . Q aH\JI\Q JJrri ruJa çaP
(Jo, )Jt!'1\ J~ -INJ1b, Ugl>/lJll'll&7 AB rÀ ),p)/lil f fo .
C- -t
At~ b~ -h A Lcf Ai
~ IIABt·h-
- ~2-
A ~
------ --
lJ :: (XII Y' I 3d
v:: (kk I yz ( fi I
W ~ (><3 I y 5 I ?} J
Vk.t--M. s: .J ![ÃBtÁLÂDJ J
c
3,~~r~doJID
• í) S-t 1MCJ>Ji '. d~s v_
dJ. ~~ ;-rrw:JtX ';Ina!',
U .-1...J J ....,4 ~ ..,. oS 7>J
jí) [J, +Uí ,;V ,IJJ. ~ [U I ('v' ,Vii J r [ U1 (1/ fIA!,
lií) [A li I ; I~ J '4 A [U », W J
~bs • Qs. VT)m1 J.MA.5-Joo, cLt V/ F I f~ ..lu!!. uM NU>UllflHI/ e r~t, mi5./e-
((j1Y}~ d- A -__~ _._
I~----------------------~.t~~----------------------------·~±~~--
~}./'t~c® ck 'IJfl&Vcx,3,ié -~~ v
'P (- Z0 {( : 5 I g ) '0 J 12 .I 13 I 15
17J - 20 12 ~ j I 4 J ~
'P2 - 2.0 r I ; & /1
'PZ - 2012 : j I jj I JE
.tz - 2.0/3 ; 2.).( J 5 I 12.. I t5
'f"SA- dt< UsTh.•. 3, 4 , /4 {rIM p"'úSil ~ ic&J", L Ig J 24
]L - 5isteYfb.. de ~&.md~
.>~,..,....~
U"' b1Ste'fY't'A JJ. Ue'\d$\o--J~ Z:» (O I L ) .[ tê1'shiuíd8 ~ ).jrY(l rlW)~ê O I
o. Ok>r6rM I ..l jjfma. '1J b"-M fl.t v,Jê1J.l)· E.. ': Nà·~ dt A~Õ~''()r J U5oJUM)a> ~pN
(1 b~ ~ z: {7 I J I k l . Ef\i5"e f&'\ e.t'~-k1 I ~ li prle.&uf ~ o- bo.N.
t ~,.,Je j.Mt dxh""rtlil1ll\ ~Il.<ho h rWOJ; 'Th1 lAlJ((JfiiJ ,~ v = (' ".r J
Y1} Sl5reYYO.. L ) ivJl\ Jif.' jW ~ ?:; O t (L I, /) e-
Pe.urruJu MU!TO ').\Po~AN1f ,1 ÂB = B- A I . ..
1>o't e)(JfrtlpQê ,- ~ 'P: (...1/3
1
- t)..l (à~ = (I )o J Z,) ;-P0v ~<a:-f .:: (O j :"'3/3)
1\ {~ : I 2:4-3)
):; _-.À
It ~ (1,2,0 J ...t ~ ~ (o I2u-tJ
. \lê)Q~dê ().!J.fX,J/Yn}JQa ~ e~li~~ÕÍ) vl:tMlJ
S1 ~W:.~ 0.$ ~(){l1I,(tl\À(i)..'J;
) ~ ~ ,
.n J ~::; f .••./\
. '3~ l+zA
4' )1J~~ JU!o.t1YW ..urrtr.(, ~<,; .1Jliv~1k:> o, pOl\-M da, irJrJdi tmtlo (pl'tYlW J.. Vt/tn) d.t
~ ~ 1.u<J.o, jJeb'~ ,u.ktt~ JItlbu .J..s. Te,,-/e ~ ~ f"1~~ dL ():).tk·
casô- -/ ..( m0J5 ro:ô..Q ~ ~JJl, dLc-~.· . "
(ii) ii ,.1. S me
Ubs : pCN\rJt VlIl bt deb ~two ~fwnh~,
lJ,6k 'V JIl À\. ~ '~~o-d~ S'oo
~ê~CÁ~ (ul'y~ U"'~'v)
As:-im '. ( 11 -~ 13/ -L ?MJJe a. (-z. ,4 ,-G)
( I J Z '/3) nõ:6 ;: p>l\o.LitJ o- (- ( ) - Z13 )
fESUMO
.Ji ..I. S mV.lI\Sab : [n /~)Jk J 10
)1.. ~ S c.~Y1C§I!lJmie.s ~ [n: f b IÃi3 ] :::O I nIb I ti ,0lf'~8)
fi. # .b J.. n: i- h ; 1ií I h J ~b7 I (lL /Ài t YfJs ~~D'7
ri Ii/) ,~fl:::5 ; 1n ,.6/~o1~rv / I n I AM Fili~1P
(li) An~
_ V J/Yfl&o ~Mt ( fl / ~ f s~ , ~oJJ.Qa5> (rt.5 1 s: - ~
-Ach().{Yl",(V AB ='B-A :::. (01013) - (.J,-',1).:. (-IIII~) ~ yt~..[
~;...>
~
'(d&Ai,aA-S Df5í(WrM
(1'f,/I1:> ..t rt, t b )
5i. ,L ÃB yW pr.nbt~e.Qa~
'T'ItRAI1LA~ rnr NÇ/VENTB- -(.n//J) ../.. n.==- b) -( n: 1f\6 )
( ;t I h J AB f s"õ.e ceflmJflJ!)
.', [n,I; ',It-; ] := O
~b!):attê~~ oU.;;' lS
5) F~enck ~-h nho.>
A) Vi:Stnmcu>' JJntf\~ 11~~ .J. JÜ-k.~ ~ -- -"...,..-...
dp, TI- z: 1I..n 1\ AP ..1l
I/it, iI
B) DiShmcio. Jmtni duoo J"tttos~"...,...,....~~
• Se. Jt l/h .~ n. = 5 4 A d,,~ 1:r (M v.;: !)
• Se '" li P ).. r1-'l.!. .,p Plf, )lIYtl f.."lli ~uol~U11\ <U )lIlYlJ. mio. J.
ccl~ lill.11 QJ51NJ,Wi.. .Jr o. ~{C'(\ F~j~ •.t.;:
• S>.. J1. rhs (<'.gnCWJl'll"b) .•• SJ. Jrfl~ .llI11 \)';1 'J'wn-be j :p<>Il& <lJ.tlllmLW:-
~ i~\ 00 dl><>D 4UQ~ cIt ~ .
s S--t, ;t. L-5 {;{)j3 SU.Y 1J)So.1> d I ~ ~ J I< : A,s.::. [Ã-:,.$ I AB
".ii /I.~s/I
II
-11
a=- ? + 2P"R .:
lã,,::. (2(0,2)+f2,2/Z)
1~4}1
~ - &tvd~ eU Vlamê(),..."...,..,.- .- ~
Um9.k1~'ir f dJ.tlf1.JTl1Í,niXde 'fll1 JJJm f&Y1k--l
(1'10& pOJ\o1b J.m-!nt 51) . fcJl oltQ.cs "'" f1mo
A e:. 1T' I C!llÍ I V:/lTí
UO'l pomW )( ~ lIl'1t-L "" 11" ~
~b6: dfà .l1)fJl~ ar oJ. ( ~c.hOO1)!D ~ pM~WCA ·~iNY'Jo
lNm(Ã da& vwU ~ V~
Ex ".1í~)(1- ~ -+ 33 - { s: O
)(:;- j- ~-3b i
x-:; t : Á -3,..
d ,:; Â
? z: f-
é)
.J
It::;; (-, ,OJO J I
À ~ z: ( -;3 ,O J J'
..(.
~ :; (-( ( I, O )
~~ ~. <\ '1&lJrirJ
i).5e Y;c~~o
Ne.S-!e ~ I {lJm QS. ~ iu: _TI 1/ ~ (!p& ptttA -
{e,Qns J J. h~ du~ ~ ih;O.id~ .•P-- ..'~JtLi:;: ~ Z-~
(cd (bl
(D.. ) tr Ii It ~ Jl C J1' ; ~ ~ A JIh 1U-ta € 11
(bl TI/I1 ctm'l n: Jé Tf í & p~-ie A ~ rkl1f
li/Se. y,r.lIC
Ne.s.+l c..Q.5.ô .A ..l.. If ~ c.J~l1LWJfYJtlD---
E.. p~ o.cJ.ar. ~ p<m{e J..t JmllYYtfl\~ ~vun.la
slSittmQ"\ 1~
G
Em e.sp~ I li n). ji .s~ pna1k
( mÚ~ipV&-) r JL..L 7/
-
1(,: 2)( -3y + 3 --f.-::,o
.n, ) .l( - -1..\
) ~ =- -r -t~A =I
b;:; /-ZA
c ) ~ JU\JthvQ ; 1JodJs x Plorr&
&-tu~ o, fêstçá& là pwrHll d{J? vt/w.v : h, (rmmw.l D.1r1J 1 Yk (rmnnJ DI 7rz)
txe'rfJp~ 7f I: X't ~ -3>-1 ( =-0
7Iz ; 2~-~.ftJ0 -4 :: O
n; ::: (f,I,-f) 1 hl:.: (2,-/16)
nJ rA0 .r p1J('D.h~d Q nt ;:;:;J (f, ~lTZ ,.~ J:.
.-.......--
~Lo'lrJIYÍi!9
5J 1MlSlll '" . 1\1i.. d."t!W;g·tfo : pr.&~
&s Flc:::> X G (o. I F/c) l.u.t JJ)~ »m lT / 1.n t
TI' } o:« b -c -I r~o '"')«(~2-)-
nz J z»: ·-6 +3c..-4 = O ~( +
ií' ~, -= ( 2, -3 I I ) .L 'f)"7Z;: (- 2I - 3 I - J) ) o: 4 b _L 4- t ; O r:r. )
LO!\é) 1f,ffTlz potE> nf ;:; - Y1l (('""",\II~G;)/ -3b ""Se -C; :0 aiv r~~. -2
iiil r~ V.lf\ A.t 1T1 :::nz. J.,. (1t1 -3b'l'5L _G~O ~) b:: 5,gt
/1 ( 'I' clJ.. cx) o, -r (5 c - Z ) '-c ·f r::; o
1).:,.. TSM' JJ lTz P()(t(rr.(b ~ ~lD O,-3tt.. . r>..3 = -l c, + (
í~~ Jm1 tr f ; Z· O -3 (-3) "t 4 - '1;: tia . " 3
'PoI'.~t~~omvb- .JJm c ~
)(= Q ~ -fÁ TI
.fi,) b 3'I y:-' -= -'1á.Á - Z.
, O~ c= ""
~v í Jt: X ~ ( (rZ ,O) f A ( - ~ I~ I /)
, 3 Ô
(h I
rr, /Iffz 1 1f( c1fz
'Po.ro. 5.'>. b,v) .bl 11( :: 1ft' ( ~ b) / -te.s-
t~ Jll VYr7 pde dl 1f' 'F"hfl1tl ~ ,
Ti z, ( eQ ~ CM'\tl\â.rJ.e-) .
í I nr = { 2 I - 3 t. f.J
\fl: .:: (J(J,r) A( 2,(1-11
.J.
~ --f,L. I
Inz :; /} J J J ( I~-! + tj + k - zk ~i -I J
z. J -( -= t=z., õ/-IJ
~\) ~o.. / Y\~~ F"ilh\u
lv) ~[J .:) Ir, 1/(1 z. .J.
I ~ < iiv!y,'lf ~ (I
11 ri /f
JlM I fl::; P 't"'Z ir?
(j,=- (2,-( si) 1" Z (-1/3 I -ZIJ J '/3 J
Ia" ('1>3 } - 'i'/3I 5/;3 ) 1
..,
n
I
\
! 'Ia (
-

Continue navegando