Question

Dados os vetores .....

Answer 1

Boa tarde Renata!

Solução!

Para resolver esse exercicio,precisa montar um sistema linear com os vetotores.

Vou chamar de:
a1=a
a2=b

$Sendo\\\\\ \vec{u}=(3,8)\\\\ \vec{v}=(2,-2)\\\\ \vec{w}=(-5,-6)$

Montando o sistema com os vetores:

$a(\vec{u})-b(\vec{v})=\vec{w}\\\\\ a(3,8)-b(2,-2)=(-5,-6)\\\\\ 3a-2b=-5\\ 8a+2b=-6\\\\\ 8a+3a=-6-5\\\\ 11a=-11\\\\ a= \frac{-11}{11}\\\\ a=-1\\\\\\ Calculo~~de~~b\\\\\\ 3a-2b=-5\\\\ 3(-1)-2b=-5\\\\ -3-2b=-5\\\\ -2b=-5+3\\\\ -2b=-2\\\\ b= \dfrac{-2}{-2} \\\\ b=1$

$\boxed{Resposta:a_{1}=-1~~a_{2}=1}$

$Prova\\\\ -1(3,8)-1(2,-2)=(-5,-6)\\\\ (-3-2)=-5\\\ -5=-5\\\\\ (-8+2)=-6\\\ -6=-6$

Boa tarde!
Bons estudos!