# Vectors, n-tuples, and headaches oh my!

1. Jan 3, 2010

### kashiark

1. The problem statement, all variables and given/known data
An n-tuple C has two representation in terms of the linearly independent pair A,B
C = (x-3)A - YB
C = -yA - (x+2)B

Solve for x and y.

2. Relevant equations
aA+bB+cC = 0
where A,B,C are linearly dependent n-tuples and a,b,c are real numbers that don't all equal 0

3. The attempt at a solution
I tried this problem about a billion different ways; however, none yielded promising results. I know the answer, and it is numerical! I don't want x and y in terms of A and B; they have numerical values. It would be helpful to explain what you're doing as you do it, but I can probably figure it out if you just show the work; laziness is something that I understand well.

2. Jan 3, 2010

### Dick

I'm not sure I get why you are confused. If A and B are linearly independent and (x-3)A-yB=-yA-(x+2)B, doesn't that mean (x-3)=(-y) and (-y)=(-(x+2))? That's two equations in two unknowns. Just solve them.

3. Jan 4, 2010

### kashiark

I guess I was over-thinking it; thanks!