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Math Help - Expression of three equation linear in Ax=b form

  1. #1
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    Expression of three equation linear in Ax=b form

    I need to express the following equation in the form of matrices A x = b

    This is an easy concept except for the fact that this system has more unknowns than equations. Should I solve for w in terms of x, y z to eliminate one variable????


    4x - 2y +z - 3w = -3
    x + y -4z + 2w = 6
    2x + 3y - 5z - w = 4

    If this were a square system there is nothing to figure out but sinc it is not...???? Thanks, Frostking
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  2. #2
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    A matrix doesnt have to be square so you can write this as normal
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  3. #3
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    Quote Originally Posted by Frostking View Post
    4x - 2y +z - 3w = -3
    x + y -4z + 2w = 6
    2x + 3y - 5z - w = 4
    Why can't you look at it this way:
    4x - 2y - 3w = -z -3
    x + y + 2w = 4z + 6
    2x + 3y - w = 5z + 4

    So you'd be solving 3 unknowns from 3 equations, in terms of z.

    Or do I need to get my head examined
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  4. #4
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    Quote Originally Posted by Frostking View Post
    I need to express the following equation in the form of matrices A x = b
    The matrix A will be the usual coefficient matrix. The matrix x will be a column vector with x, y, z, and w. The matrix b will be a column vector with the answer values.
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  5. #5
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    Quote Originally Posted by Wilmer View Post
    Why can't you look at it this way:
    4x - 2y - 3w = -z -3
    x + y + 2w = 4z + 6
    2x + 3y - w = 5z + 4

    So you'd be solving 3 unknowns from 3 equations, in terms of z.

    Or do I need to get my head examined
    That would result in three equations in three variables that could then be solve for x,y, and w in terms of z. Perfectly valid.

    (Of course, it probably wouldn't hurt to have your head examined!)
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    (Of course, it probably wouldn't hurt to have your head examined!)
    Your brains are expensive...never been used
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