Question

Realice las siguientes operaciones, dados los vectores: u= (-3,2,1,0) v=

(5,-3,6,1) y w= (3,-2,8,1). Encontrar:

a) v-w

b) 2u+8v


c) 6(u-2v)


d) (4v-w) – (5u+v)

Answer 1

PREGUNTA

Realice las siguientes operaciones, dados los vectores:

u= (-3,2,1,0), v= (5,-3,6,1) y w= (3,-2,8,1).

Encontrar:

a) v-w  

b) 2u+8v  

c) 6(u-2v)

d) (4v-w) – (5u+v)

SOLUCIÓN

Hola!! :D

a)

$v - w = (5,-3,6,1) - (3,-2,8,1) \\\\v -w = (5-3, -3-(-2),6-8,1-1 )\\\\\boxed{\boldsymbol{v-w= (2,-1,-2,0)}}$

b)

$2u + 8v = 2(-3,2,1,0) + 8(5,-3,6,1)\\\\2u + 8v =(-6,4,2,0) + (40,-24,48,8)\\\\2u + 8v = (-6+40,4-24,2+48,0+8)\\\\\boxed{\boldsymbol{2u + 8v =(34, -20,50,8)}}$

c)

$6(u - 2v)= 6[(-3,2,1,0)-2(5,-3,6,1)]\\\\6(u - 2v)= 6[(-3,2,1,0)-(10,-6,12,2)]\\\\6(u - 2v)= 6[(-3-10,2+6,1-12,0-2)]\\\\6(u - 2v)=6(-13,8,-11,-2)\\\\\boxed{\boldsymbol{6(u - 2v)= (-78,48,-66,-12)}}$

d)

$(4v-w)-(5u +v) = [4(5,-3,6,1)-(3,-2,8,1)]-[5(-3,2,1,0)+(5,-3,6,1)]\\\\(4v-w)-(5u +v) =[(20,-12,24,4)-(-3,-2,8,1)]-[(-15,10,5,0)+(5,-3,6,1)]\\\\(4v-w)-(5u +v) =[(20+3,-12+2,24-8,4-1)]-[(-15+5,10-3,5+6,0+1)]\\\\(4v-w)-(5u +v) =(23,-10,16,3)-(-10,7,11,1)\\\\(4v-w)-(5u +v) =(23+10,-10-7,16-11, 3-1)\\\\\boxed{\boldsymbol{(4v-w)-(5u +v) =(33,-17,5,2)}}$