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Math Help - I have to show this proof for the matrix inverse theorem

  1. #1
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    Lightbulb I have to show this proof for the matrix inverse theorem

    I cannot use the matrix inverse theorem, yet I have to show this, thanks in advance.

    If the equation Ax = b has at least one solution for each b in Rn, then the equation Ax = 0 has only the trivial solution.

    thanks in advance
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  2. #2
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    Re: I have to show this proof for the matrix inverse theorem

    Isn't it because the only matrix you could multiply x by to get the a zero vector is the zero matrix, and that the determinant of the zero matrix is 0?
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