Question

Dados os vetores u= (3,−1) v= (-1,2) e w= (3,0). determinar o vetor
x em cada caso.

Answer 1

Resposta:

a) Primeiro substituímos :

3 x+3.(-1,2)=2.(3,-1)-x+5/4.(3,0)

3 x+(-3,6)=(6,-2)- x+(15/4,0)

Isolamos as incógnitas x :

3x+x=(6,-2)+(15/4,0)-(-3,6)

4x = (6+15/4+3,-2+0-6)

4x=(51/4,-8)

x=(51/4:4, -8:4)

x=(51,-2)

b) 5x + 2.(-1,2)-1/3(3,-1)=3((3,-1)+x+3/5(3,0))

5x+(-2,4)-(1,-1/3)=3((3,-1)+x+(9/5,0)

5x+(-3,13/3)=(9,-3)+3x+(27/5,0)

Isolamos o x :

5x-3x=(9,-3)+(27/5,0)-(-3,13/3)

2x=(9+27/5+3,-3+0-13/3)

2x=(87/5,-22/3)

x =(87/5:2, -22/3 :2 )

x=(87/10,-22/6)

x=(87/10,-11/3)

Bons estudos !