Question

Dados os vetores u = (2, 3, -1), v = (1, -1, 1) e w = (-3, 4, 0), determinar o vetor x tal que (3u -v+x=4x+2w )

Answer 1

$x=(a,b,c)\\\\ 3u-v+x=4x+2w\\ 3u-v=3x+2w\\\\ 3(2,3,-1)-(1,-1,1)=3(a,b,c)+2(-3,4,0)\\ (6,9,-3)+(-1,1,-1)=(3a,3b,3c)+(-6,8,0)\\ (5,10,-4)-(-6,8,0)=(3a,3b,3c)\\ (3a,3b,3c)=(11,2,-4)\\\\ 3a=11 \rightarrow a = \frac{11}{3}\\ 3b=2 \rightarrow b = \frac{2}{3}\\ 3c=-4 \rightarrow c = \frac{-4}{3}\\\ x=(\frac{11}{3},\frac{2}{3}, \frac{-4}{3})$