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Math Help - Find Ax = 0, prove this is only solution..

  1. #1
    Junior Member
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    adelaide
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    Find Ax = 0, prove this is only solution..

    Hi, I have a matrices question..

    Suppose CA = I(n).
    Find a solution to Ax = 0, and prove that this i s the only solution, justify.

    I struggle with the way some maths questions are worded.

    As I understand this is a homogeneous equation, and they have at least one solution, the trivial solution where x = 0.

    So I'm to show that there is no non trivial solution and x must equal 0?

    If this reasoning is correct then I don't fully understand what CA = I(n) means and how to use it?

    Can someone enlighten me?
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  2. #2
    MHF Contributor

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    Tejas
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    Re: Find Ax = 0, prove this is only solution..

    If CA = I, we have:

    Ax = 0

    C(Ax) = C(0) = 0

    (CA)x = 0

    Ix = 0

    x = 0.
    Thanks from camjerlams
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