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Math Help - Singular Matrices Theorem

  1. #1
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    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?
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  2. #2
    A Plied Mathematician
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    What have you tried so far? I would probably do a proof by contradiction.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    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?
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  4. #4
    A Plied Mathematician
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    I'm asking what you could do if the matrix had an inverse. Take a look at your equation there.
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