Question

Dados os vetores u=(3,-1) e v=(-1,2), determinar o vetor x tal que: 4.(u-v) + (1/2)x = 2u - x


(-20/3 , -20/3)
(-3/20 , 20/3)
(20/3 , -20/3)
(-20/3 , 20/3)
(20/3 , 20/3) e umas dessas so nao se qual

Answer 1

$4(U-V)+ \frac{1}{2}W=2U-W \\ \\ 4[3-(-1)]+ \frac{x}{2} =2*3-x \\ 16+ \frac{x}{2} =6-x \\ 32+x=12-2x \\ 4x=12-32 \\ 4x=-20 \\ x= -\frac{20}{4} \\ \\ 4[(-1)-2]+ \frac{y}{2} =2(-1)-y \\ -12+ \frac{y}{2} =-2-y \\ -24+y=-4-2y \\ 4y=20 \\ y= \frac{20}{4}$
W(-20/4,20/4)