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  1. #1
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    gauss jordan help

    Ok here I am working on this problem for like 3 hours to no avail.

    x1 + x2 = 1

    -x1 + x2 + x3 = -1

    -1x2 + x3 = 3


    I am trying to solve this in matrix form and get the point of multiplaying a cooefficiant but applying it to this set is baffling my mind. Any insights?


    is the matrix

    1 1 0
    -1 1 0
    0 -1 1
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  2. #2
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    Quote Originally Posted by wonderstrike View Post
    Ok here I am working on this problem for like 3 hours to no avail.

    x1 + x2 = 1

    -x1 + x2 + x3 = -1

    -1x2 + x3 = 3


    I am trying to solve this in matrix form and get the point of multiplying a coefficient but applying it to this set is baffling my mind. Any insights?


    is the matrix

    1 1 0
    -1 1 0
    0 -1 1
    You should use an "augmented" matrix, with an extra column consisting of the coefficients on the right=hand side of the equations. So the matrix is \begin{bmatrix}1&1&0&1\\ -1&1&1&-1\\ 0&-1&1&3\end{bmatrix}. Now apply the Gauss–Jordan process to the matrix, and then you should be able to read off the solution.
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  3. #3
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    <br /> <br />
\begin{bmatrix}1&1&0&1\\ 0&1&.5&0\\ 0&0&1&2\end{bmatrix}<br /> <br /> <br />

    <br />
\begin{bmatrix}1&0&0&2\\ 0&1&0&-1\\ 0&0&1&2\end{bmatrix}

    have I broken this down right? so the answer would be the last column 2,-1,2

    ?
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  4. #4
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    Quote Originally Posted by wonderstrike View Post
    <br /> <br />
\begin{bmatrix}1&1&0&1\\ 0&1&.5&0\\ 0&0&1&2\end{bmatrix}<br /> <br /> <br />

    <br />
\begin{bmatrix}1&0&0&2\\ 0&1&0&-1\\ 0&0&1&2\end{bmatrix}

    have I broken this down right? so the answer would be the last column 2,-1,2

    ?
    That is correct (as you could check for yourself by substituting 2, –1, 2 for x_1,x_2,x_3 in the original equations).
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