Question

Escreva w=(2,-1,6) como combinação linear de u=(3,-1,1),v(1,2,-1) e r(0,2,5)

Answer 1

Resposta:

$\boxed{W=\frac{41}{43}u-\frac{37}{43}v+\frac{36}{43}r}$

Explicação passo-a-passo:

Seja  (2,-1,6) de vetor W

W=(2,-1,6)

u=(3,-1,1)

v=(2,-1,1)

r=(0,2,5)

Combinação

W=a*(3,-1,1)+b*(1,2,-1)+c*(0,2,5)

sendo u=a, b=v e c=r

(2,-1,6)=(3a,-a,a)+(b,2b,-b)+(0,2c,5c)

(2,-1,6)=(3a+b,-a+2b+2c,a-b+5c)

Escalonado

{3a+b=2=

{-a+2b+2c= -1 ==>

{a+-b+5c= 6===>

$\boxed{W=\frac{41}{43}u-\frac{37}{43}v+\frac{36}{43}r}$