Question

Sejam os vetores u=(3,-1) e v =(-1,2), resolva a equação 4u-2v+3w=2u-w, o vetor w é:

Escolha uma:
A) w=(2,2)
B) w=(-2,1)
C) w=(1,-1)
D) w=(-2,2)
E) w=(1,2)

Answer 1

$\mathtt{4u-2v+3w=2u-w}\\\mathtt{3w+w=2v+2u-4u}\\\mathtt{4w=2v-2u\div(4)}$

$\mathtt{w=\dfrac{1}{2}v-\dfrac{1}{2}u}$

$\mathtt{w=\dfrac{1}{2}(-1,2)-\dfrac{1}{2}(3,-1)}$

$\mathtt{w=(-\dfrac{1}{2}, 1)-(\dfrac{3}{2},-\dfrac{1}{2})}$

$\mathtt{w=(-2,\dfrac{3}{2})}$

Answer 2

Resposta:

4u-2v+3w=2u-w

4u-2u-2v=-3w-w

2u-2v=-4w

u-v=-2w

v-u=2w

(-1,2)-(3,-1)=2w

(-1-3 ; 2+1) =2w

(-4 ; 3)=2w

w=(-2 ; 3/2)