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Math Help - solving a system using A^-1

  1. #1
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    May 2010
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    7

    solving a system using A^-1

    Let A =

    1 0 -1
    2 1 -2
    0 1 1

    find A^-1 of the above matrix using inverse matrices and hence solve the bottom 2 systems:

    x - z = 3
    2x + y - 2z = 0
    y + z = 15

    2x - y = 1
    3x - y + z = -2
    2x - y + z = 3

    i got A^-1 =
    3 -1 1
    -2 1 0
    2 -1 1

    I solved for system 1, how do I solve for system 2 can you please demonstrate.
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  2. #2
    Newbie
    Joined
    May 2010
    Posts
    4
    Multiply the first equation by -1 and rearrange the system.
    2x - y = 1 |*(-1)
    3x - y + z = -2
    2x - y + z = 3

    becomes

    3x - y + z = -2
    -2x + y = -1
    2x - y + z = 3

    Then you solve the system like the you solved the first one.
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