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Math Help - Gaussian Method

  1. #1
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    Question Gaussian Method

    I want to know the row operations to solve this question.

    2 x-7y+4 z=9

    x+9y-6z=1

    -3x+8y+5z=1

    First row operation i used is 2*R2-R1 then i used 3*R2+R3 but now i m dont know what to do to.
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  2. #2
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    Re: Gaussian Method

    Quote Originally Posted by haftakhan View Post
    I want to know the row operations to solve this question.

    2 x-7y+4 z=9

    x+9y-6z=1

    -3x+8y+5z=1

    First row operation i used is 2*R2-R1 then i used 3*R2+R3 but now i m dont know what to do to.
    first let's write this as an augmented matrix

    $\begin{array}{cccc}
    2x &-7y &+4z &=9 \\
    x &+9y &-6z &=1 \\
    -3x &+8y &+5z &=1
    \end{array} \Rightarrow$


    $\left(
    \begin{array}{ccccc}
    2 &-7 &4 &|&9 \\
    1 &9 &-6 &|&1 \\
    -3 &8 &5 &|&1
    \end{array}\right)$

    swap R1, R2

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    2 &-7 &4 &|&9 \\
    -3 &8 &5 &|&1
    \end{array}\right)$

    R2 --> R2 - 2R1

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    0 &-25 &16 &|&7 \\
    -3 &8 &5 &|&1
    \end{array}\right)$

    R3 --> R3 + 3R1

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    0 &-25 &16 &|&7 \\
    0 &35 &-13 &|&4
    \end{array}\right)$

    R3 --> 5R3 + 7R2

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    0 &-25 &16 &|&7 \\
    0 &0 &47 &|&69
    \end{array}\right)$

    R2 --> R2/(-25)

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    0 &1 &-16/25 &|&-7/25 \\
    0 &0 &47 &|&69
    \end{array}\right)$

    R3 --> R3/47

    $\left(
    \begin{array}{ccccc}
    1 &9 &-6 &|&1 \\
    0 &1 &-16/25 &|&-7/25 \\
    0 &0 &1 &|&69/47
    \end{array}\right)$

    you can either solve it from here using back substitution or continue to reduce it.
    Thanks from haftakhan
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  3. #3
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    Posts
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    Re: Gaussian Method

    x=182/47
    y=31/47
    z=69/47
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