p3 poli 2006

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Questão 2: Em JR5considereossubconjuntos:
C1 ={(O,1,1,1,O);(0,2,1,O,I)} e
C2={(1,1,1,0,1);(1,0,1,1,0)}
e ossubespaçosTI =[C1] e T2=[C2].
(a) (1,5)AcheumabaseedêadimensãodeTI nT2.
(b) (1,5)AcheumabasedeTI +T2contidaemC1UC2.
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Questão 3: Sejamoespaçovetoria!C ={f : IR -t IR/fé contínua}eo subespaço:
V =[1+ Ixl, sen2x, cos2X, Ixl].
(a) (2,0)DetermineumabasedosubespaçoS ={f E V/fé derivável}.
(b) (1,5)Mostrequesen2x E S ecompleteo conjunto{sen2x}aumabasedeS.
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s~ a.X (v-A.}.
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Pl =2x- X2 +X4
P2 =3X2 - X3 + 2X4
P3=4x- 5x2+X3
P4 =1+x +X2
(a) (1,5)DetermineumabasedeA contidaem{PbP2,P3,P4}.
(b) (2,0)SejaP = mx - mx2+x3 +x4,m E ]R. Determinem tal queP E A.
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Questão 2: Em JR5considereossubconjuntos:
AI ={(1,1,1,0,1);(1,0,1,1,O)}e
A2={(0,1,1,1,0);(0,2,1,0,1)}
eossubespaçosSI = [AI] e S2= [A2].
(a) (1,5)Acheumabaseedêa dimensãodeSI nS2'
(b) (1,5)AcheumabasedeSI +S2contidaemAI UA2'
Cl) ~'" f\ Sg., ::: 1 [)(-11Xz}X 3>'X4-)y.~)/.3 ÀI\) À2/ fA" ,)'\'1-t- ~c:..s-rn
C~"x'I~ô1)<4,~.r)'" ?,1 (1,1,',o,1)t >-2(1,0,'},O)~ fJ'-< (.0,'/,1,O) +)'<2(O,L,I,o,I) ~
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Questão3: Sejamo espaçovetorialC={f : IR -+IRI f écontínua}eo subespaço:
V =[1+ Ixl, sen2x, sen2x, Ixl].
(a) (2,0)DetermineumabasedosubespaçoS ={f E VIf éderivável}
(b) (1,5)Mostrequecos2x E S ecompleteoconjunto{cos2x}aumabasedeS.
1. + I)C. { .- (X I.=: 1 ~ ~C~
V=-Ci J SRAA::LX)~X j 1)1.i]
~ S ~ ly.\4: S
s.
_, B.+ b + .!..c .:: U"/ t5L
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x~ Ir
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E 1'-M'lC~ B [LI
5
b)
2.
i - $ .~\A X
s.
eo ,1/t;MQ {,~ "/1/1/1 S -:=:. 3 -e
C,o.V\ti~<A'- ~ cr A.
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C ' .i + b. S.l-v1 Z X -+C. s
2. >< E-IK
X -=0 r 6'-<..-1,) .
Pl = 2- x - 5x2
P2= 3 - 2X2
P3= 1+ x + X2+ X3
P4= 8 - x - 9x2
(a) (1,5)Determineumabasede A contidaem {Pl,P2,P3,P4}.
(b) (2,0)Paraqualvalordem E IR opolinômioP = 1- 2x+mx2/I.pertencea A?
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