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Thread: [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

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

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


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

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

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

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


    In your case you have

    $\displaystyle A = \left[\begin{matrix}
    1 & -4 & 3 & -2\\
    3 & -2 & 1 & -4\\
    -4 & 3 & -2 & 1\\
    -2 & 1 & -4 &3 \end{matrix}\right]$

    and

    $\displaystyle \mathbf{b} = \left[\begin{matrix}
    9 \\
    -13 \\
    -4 \\
    -10 \end{matrix} \right]$.


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