Question

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?

Answer 1

`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))`