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Math Help - System of equations

  1. #1
    Senior Member
    Joined
    Apr 2010
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    487

    System of equations

    The question:
    Show that the system of equations x + y + 2z = a, x + z = b, and 2x + y + 3z = c are consistent if and only if c = a + b.

    My attempt:
    I put the equations into an augmented matrix, and did row operations to produce row-echelon form. I got the following:

    1 1 2 | a
    0 -1 -1 | b - a
    0 0 0 | c - 2b

    To be consistent, the third row must not imply no solutions (i.e. LHS must equal RHS). But this gives me c = 2b, not c = a + b. What am I doing wrong? Thanks!
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  2. #2
    Junior Member
    Joined
    Oct 2009
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    You must have gone wrong in your row reduction. I row reduced the matrix and I satisfied the condition. Check over your working, you might see where you went wrong.
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  3. #3
    Senior Member
    Joined
    Apr 2010
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    Ahh yes, I made an error with the very last row. Thanks!
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