Originally Posted by

**cottontails** "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 $\displaystyle -\beta$ in the LHS parentheses and $\displaystyle -\alpha$ 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.)