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Math Help - Element Row Operation problem

  1. #1
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    Element Row Operation problem

    Element Row Operation problem-codecogseqn-1-.gif

    Find the value of a , b , c and d.
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  2. #2
    Member kalyanram's Avatar
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    Re: Element Row Operation problem

    Consider the augmented matrix \left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 3 & : & 7\\2 & 0 & 0 & -4 & : & 6\\ \end{array} \right)

    R_4 \rightarrow \frac{R_4 - 2R_1 - 2R_2 + 2R_3}{2}
    \left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 3 & : & 7\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)

    R_3 \rightarrow R_3 - 3R_4
    \left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 1 & 0 & : & 1\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1& : & 1\\ \end{array} \right)

    R_2 \rightarrow R_2 - R_3
    \left( \begin{array}{cccccc}1 & -1 & 0 & 0 & : & 8\\0 & 1 & 0 & 0 & : & -3\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)

    R_1 \rightarrow R_1 + R_2
    \left( \begin{array}{cccccc}1 & 0 & 0 & 0 & : & 5\\0 & 1 & 0 & 0 & : & -3\\0 & 0 & 1 & 0 & : & 4\\0 & 0 & 0 & 1 & : & 1\\ \end{array} \right)

    We have

    \left( \begin{array}{cccc}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\\ \end{array} \right) \left( \begin{array}{c}a\\b\\c\\d\\ \end{array} \right) = \left( \begin{array}{c}5\\-3\\4\\1\\ \end{array} \right)

    a=5, b=-3, c=4, d=1.
    Last edited by kalyanram; September 10th 2012 at 05:54 AM.
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