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Math Help - Linear Equation Using Matrices

  1. #1
    Junior Member
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    Linear Equation Using Matrices

    Solve the following system, where a, b, and c are constants:

    x1 + x2 + x3 = a
    2x1 + 2x3 = b
    3x2 + 3x3 = c

    If I put this into a matrix I get:
    1 1 1 | a
    2 0 2 | b
    0 3 3 | c

    I'm really not sure where to go from here because it seems to me like row 2 and 3 will cancel out making b and c equal 0, but I'm not really experienced with this and I'm not even sure what I'm trying to obtain in the end.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Adrian View Post
    Solve the following system, where a, b, and c are constants:

    x1 + x2 + x3 = a
    2x1 + 2x3 = b
    3x2 + 3x3 = c

    If I put this into a matrix I get:
    1 1 1 | a
    2 0 2 | b
    0 3 3 | c

    I'm really not sure where to go from here because it seems to me like row 2 and 3 will cancel out making b and c equal 0, but I'm not really experienced with this and I'm not even sure what I'm trying to obtain in the end.

    Thanks
    subtract twice row 1 from row 2:

    Code:
    1  1  1 | a
    0 -2  0 | b-2a
    0  3  3 | c
    Now add 3/2 times row 2 to row 3:


    Code:
    1  1  1 | a
    0 -2  0 | b-a
    0  0  3 | c + (3/2)(b-2a)
    Now solve by back substitution.

    RonL
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