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Math Help - Augmented matrix

  1. #1
    Junior Member
    Joined
    Mar 2008
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    Augmented matrix

    Hi everyone.
    I need to consider the following system of equations, where m belong to R is an unknown constant:
    x + 2z = 1
    2x + y + 3z = m
    -2x + my - 5z = -3

    How to write down augmented matrix of the system and transform it into reduced row echelon form.????
    Is it any chance to find the value of m which the system has:
    no solution,
    infinitly many solutions or
    unique solution???

    Thank you
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
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    Quote Originally Posted by Snowboarder View Post
    Hi everyone.
    I need to consider the following system of equations, where m belong to R is an unknown constant:
    x + 2z = 1
    2x + y + 3z = m
    -2x + my - 5z = -3

    How to write down augmented matrix of the system and transform it into reduced row echelon form.????
    Is it any chance to find the value of m which the system has:
    no solution,
    infinitly many solutions or
    unique solution???

    Thank you
    If we wrote this system in matrix form, we would get \left[\begin{array}{ccc}1&0&2\\2&1&3\\-2&m&-5\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}1\\m\\-3\end{array}\right], where m\in\mathbb{R}

    This matrix equation can be written in augmented form:

    \left[\begin{array}{ccc}1&0&2\\2&1&3\\-2&m&-5\end{array}\right]\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}1\\m\\-3\end{array}\right]\implies\left[\begin{array}{ccccr}1&0&2&:&1\\2&1&3&:&m\\-2&m&5&:&-3\end{array}\right]

    Your goal is this:

    Get \left[\begin{array}{ccccr}1&0&2&:&1\\2&1&3&:&m\\-2&m&5&:&-3\end{array}\right] into this form: \left[\begin{array}{ccccr}1&0&0&:&x_0\\0&1&0&:&y_0\\0&0&  1&:&z_0\end{array}\right], where x_0,~y_0,~\text{and }z_0 are the solutions.

    Try to take it from here. If you get stuck, let us know.

    --Chris
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  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    56
    ok so i've got:

    {{1,0,0,2m-1},{0,1,0,-1},{0,0,1,1-m}}

    how to find values of m for which the system has:

    no solution
    infinitly many solutions
    a unique solution
    ???

    thx for help
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