Let u = <-3, 2>, v = <3, 0>, and w = <5, 2>. Find the vector x that satisfies 8u-v+x=3x+w. In this case, vector x is?

I've been working on this homework problem for a while, and I keep getting wrong answers (they're online so I know if I'm doing them right or not). I know you have to solve put u, v, and w into what is known of the equation, then try to reorganize and solve for <x1, x2>, but I can't get anything to work... maybe I'm not actually going about this correctly?

1 Answer
Nov 12, 2017

color(blue)(x=((-16),(7)))

Explanation:

Vectors:

u = ((-3),(2)) , v=((3),(0)) , w=((5),(2)) , x=((x_1),(x_2))

First rearrange 8u-v+x=3x+w and get the unknown vector on one side.

8u-v-w=3x-x

8u-v-w=2x

8((-3),(2))-((3),(0))-((5),(2))=2((x_1),(x_2))

((-24),(16))-((3),(0))-((5),(2))=2((x_1),(x_2))

((-32),(14))=2((x_1),(x_2))

1/2((-32),(14))=((x_1),(x_2))

((-16),(7))=((x_1),(x_2))

x_1=-16
x_2=7

color(blue)(x=((-16),(7)))

You can check this with original statement.

8u-v+x=3x+w

8((-3),(2))-((3),(0))+((-16),(7))=3((-16),(7))+((5),(2))

((-43),(23))=((-43),(23))