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Thread: Row reduced echelon form and its meaning

  1. #1
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    Row reduced echelon form and its meaning

    Hey.

    I have the following question to solve:

    * Given a matrix A that is size m x n and m>n.
    Let R be the RREF that we get by Gaussian elimination of A.
    Prove that the system equation Ax=0 has only one solution iff in every column of R there is a leading element.

    I have some answer of intuition so I'm not really sure,
    Let's assume that we had R with some free variable, and we know(?) that any free variable has a degree of freedom which means that it yields infinite number of solutions.

    Now, I am not sure again about the establishment of this proof and to what extent it's accurate. Moreover, I am not if it proves the point of iff (equivalence).

    Another similar question, but I have no idea what it means:

    * Given a matrix A that is size m x n and m>n.
    Let R be the RREF that we get by gaussian elimination of A.
    Prove that for every the system equation Ax=b has a solution iff R doesn't have zero rows.

    Thank you!
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  2. #2
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    Re: Row reduced echelon form and its meaning

    Rows of zeros
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