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Math Help - [SOLVED] using matrices to solve for a system of equations using gaussian elimination

  1. #1
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    [SOLVED] using matrices to solve for a system of equations using gaussian elimination

    my system of equations is

    x-4y+3z-2w=9
    3x-2y+z-4w= -13
    -4x+3y-2z+w= -4
    -2x+y-4z+3w=-10

    my augmented matrix is
    1 -4 3 -2 9
    3 -2 1 -4 -13
    -4 3 -2 1 -4
    -2 1 -4 3 -10

    i don't know how to plug this into my calculator to get an answer, but i got these answers using the row operations:
    x= -19.5
    y= -4.5
    z= 0.5
    w= 4.5

    these answers don't seem correct, so i was wondering if anyone could tell me the actual answers when plugged into the calculator, so i could figure out what i did wrong or ask for more help.
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  2. #2
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    Quote Originally Posted by somanyquestions View Post
    my system of equations is

    x-4y+3z-2w=9
    3x-2y+z-4w= -13
    -4x+3y-2z+w= -4
    -2x+y-4z+3w=-10

    my augmented matrix is
    1 -4 3 -2 9
    3 -2 1 -4 -13
    -4 3 -2 1 -4
    -2 1 -4 3 -10

    i don't know how to plug this into my calculator to get an answer, but i got these answers using the row operations:
    x= -19.5
    y= -4.5
    z= 0.5
    w= 4.5

    these answers don't seem correct, so i was wondering if anyone could tell me the actual answers when plugged into the calculator, so i could figure out what i did wrong or ask for more help.
    Note that if you have a system of equations of the form

    A\mathbf{x} = \mathbf{b}

    then you can use Matrix Algebra to solve for \mathbf{x}.


    A\mathbf{x} = \mathbf{b}

    A^{-1}A\mathbf{x} = A^{-1}\mathbf{b}

    I\mathbf{x} = A^{-1}\mathbf{b}

    \mathbf{x} = A^{-1}\mathbf{b}.


    In your case you have

    A = \left[\begin{matrix}<br />
1 & -4 & 3 & -2\\<br />
3 & -2 & 1 & -4\\<br />
-4 & 3 & -2 & 1\\<br />
-2 & 1 & -4 &3 \end{matrix}\right]

    and

    \mathbf{b} = \left[\begin{matrix}<br />
9 \\<br />
-13 \\<br />
-4 \\<br />
-10 \end{matrix} \right].


    So enter these matrices into your calculator and then calculate A^{-1}\mathbf{b}.
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