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Math Help - Proof for matrix

  1. #1
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    Proof for matrix

    ok this was confusing me so any help is appreicated.

    suppose A is a n by n matrix. show that the rank of A is n only if the AX = 0 has just the trivial solution.
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  2. #2
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    Quote Originally Posted by buckaroobill View Post
    ok this was confusing me so any help is appreicated.

    suppose A is a n by n matrix. show that the rank of A is n only if the AX = 0 has just the trivial solution.
    Meaning A has n linearly independent coloums vectors.
    Thus, they form a basis. Thus, a unique representation.
    Since expressing the zero coloum is possible trivially it is the only solution for it must be unique.
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  3. #3
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    What do you mean by "linearly independent"?
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  4. #4
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    Quote Originally Posted by buckaroobill View Post
    What do you mean by "linearly independent"?
    The coloums of the matrix are linearly independent.
    Because Rank(A)=n.
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