Question

Dados os vetores u= (1,2,-3), v= (2,0,-1) e w= (3,1,0), determine o vetor x de modo que x.u = -16, x.v =0, e x.w= 3.

Answer 1

$x=(x_1,x_2,x_3)$

$x\cdot u=(x_1,x_2,x_3)\cdot(1,2,-3)=x_1+2x_2-3x_3=-16$

$x\cdot v=(x_1,x_2,x_3)\cdot(2,0,-1)=2x_1-x_3=0$

$x\cdot w=(x_1,x_2,x_3)\cdot(3,1,0)=3x_1+x_2=3$

$\left[\begin{array}{cccc}1&2&-3&-16\\2&0&-1&0\\3&1&0&3\end{array}\right] \sim \left[\begin{array}{cccc}1&0&0&2\\0&1&0&-3\\0&0&1&4\end{array}\right]$

Entao:

$x=(2,-3,4)$