"Suppose

**x** and

**y** are linerarly independent vectors satisfying the following vector equation:

-4

**x** + α(

**x**+

**y**) = β(

**x**-3

**y**).

Find α and β.

I tried solving the vector equation however, I can only find a correctly and as for β, it is the wrong sign. So, I am pretty sure I made at least some error in my working.

Working:

-> (-4 + α + β)

**x** = (α - 3β)

**y** It must be in the LHS parentheses and in the RHS's one.

Tonio
-> -4 + α + β = 0 = 2 - 3B

-> α + B = 4, α - 3β = 0

-> β = 4 - α, α - 3(4 - α) = α - 12 + 3α = 4α - 12

-> α = 3, B = 1

(β is supposed to be -1 so, I know I made some error there but I'm unsure as to what I did incorrectly though.)