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Math Help - How do I find the bases for row(A), col(A) and null(A)?

  1. #1
    s3a
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    How do I find the bases for row(A), col(A) and null(A)?

    Given matrix A = ([1,0,-1],[1,1,1]), how do I find the bases for row(A), col(A) and null(A)?

    I know this is very simple for you guys but I am struggling to keep up with my work load and would really appreciate it if someone could explain it to me.

    Thanks!
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  2. #2
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    First you have to reduce your matrix to row echelon form. The nonzero rows of this reduced matrix form a basis for row(A). What are they?

    Now the columns of this reduced matrix wih leading 1's identify the pivot columns of your original matrix. And these form a basis for col(A). What are they?

    Then the canonical solutions of Ax=0 form a basis for null(A). These are readily obtained from the system Rx=0, where R is the reduced matrix of A).
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