Question

escrever se possivel o vetor v=(-1,13,-7) como combinaçao linear de u=(1,-3,2)e u=(2,4,-1).

Answer 1

Boa noite Santos!

Solução!


$\boxed{\vec{v}=a\vec{u}+a\vec{u}}$

$(-1,13,-7)=a(1,-3,2)+a(2,4,-1)\\\\\\ (-1,13,-7)=(a,-3a,2a)+(2a,4a,-a)\\\\\\ (-1,13,-7)=(3a,a,a)\\\\\\ 3a=-1\\\\\ a= \dfrac{-1}{3}\\\\\\ a=13\\\\\\ a=-7$

$Fazendo~~a~~prova\\\\ \vec{v}=\vec{a} \\\\\\ (-1,13,-7)=(3a,a,a)\\\\\\ (-1,13,-7)=(3.( \frac{-1}{3}),13,-7)\\\\\\ (-1,13,-7)=(-1,13,-7)$

Resultando da combinação!

$\vec{a}=( \frac{-1}{3},13,-7)$

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Bons estudos!