Thread: Linearly independent vectors

"Suppose x and y are linerarly independent vectors satisfying the following vector equation:
-4x + α(x+y) = β(x-3y).
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
-> -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.)

Originally Posted by cottontails

"Suppose x and y are linerarly independent vectors satisfying the following vector equation:
-4x + α(x+y) = β(x-3y).
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.)

.