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Math Help - Matrix Inverse solving system of equations

  1. #1
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    Matrix Inverse solving system of equations

    Given
    A =
    1 0 -2
    3 1 -6
    0 1 1

    I have worked out the inverse matrix and I have to use it to solve the system of equations
    3x-y = 5
    7x - 2y + 2z = 3
    3x - y + z = 7

    I can see that this is the inverse matrix, with rows 1 and 2 swapped (and -R1) but I don't know how this affects solving the equations. I have to use the inverse to solve. I really would like to understand what's happening here, rather tan just the answer. I'd appreciate any help.

    Thanks
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  2. #2
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    Quote Originally Posted by sydney View Post
    Given
    A =
    1 0 -2
    3 1 -6
    0 1 1

    I have worked out the inverse matrix and I have to use it to solve the system of equations
    3x-y = 5
    7x - 2y + 2z = 3
    3x - y + z = 7

    I can see that this is the inverse matrix, with rows 1 and 2 swapped (and -R1) but I don't know how this affects solving the equations. I have to use the inverse to solve. I really would like to understand what's happening here, rather tan just the answer. I'd appreciate any help.

    Thanks
    Re-write your equations as:

    7x - 2y + 2z = 3
    -3x + y = -5
    3x - y + z = 7

    In matrix form you have AX = B \Rightarrow X = A^{-1} B where A is the coeffcient matrix. And the given matrix is the inverse of the coefficient matrix ....
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  3. #3
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    Thanks

    Thank you very much. I knew it had to do with something like that but I just hadn't mutliplied R2 equation thru by the negative!

    Really appreciate your help.
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