Thread: Singular Matrices Theorem

Let A be an n x n (square) matrix and let x and y be vectors in all real numbers. Show that if Ax=Ay and x does not equal y, then the matrix A must be singular.

How do I start on this problem?

What have you tried so far? I would probably do a proof by contradiction.

Originally Posted by Ackbeet

What have you tried so far? I would probably do a proof by contradiction.

That's the problem, I never learned how to prove a matrix is nonsingular or singular. I know what they mean, that they have an inverse or don't.
Are you saying that I should try to show that it has an inverse? Or can I just do this by trying to find a determinate which is zero?

I'm asking what you could do if the matrix had an inverse. Take a look at your equation there.