Question

dados os vetores u (2,-3) e v= (-3,5) determinar o vetor w tal que:2(u-v)+0,5w= 3u-w

Answer 1

$2(u-v)+ \displaystyle \frac{1}{2}w=3u-w \\ \\ 2u-2v+\frac{1}{2}w-3u+w=0 \\ \\ -u-2v+\frac{3}{2}w=0 \\ \\ \frac{3}{2}w=u+2v \\ \\ w= \frac{u+2v}{ \frac{3}{2} } \\ \\ w= \frac{2}{3} \cdot (u+2v) \\ \\ w=\frac{2}{3} \cdot [(2,-3)+2(-3,5)] \\ \\ w=\frac{2}{3} \cdot [(2,-3)+(-6,10)] \\ \\ w=\frac{2}{3} \cdot (-4,7) \\ \\ \boxed{\boxed{w=( -\frac{8}{3} , \frac{14}{3} )}}$