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Math Help - Solutions to these matrices

  1. #1
    Member zzizi's Avatar
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    Solutions to these matrices

    Hi

    This may be basic, but i'd really appreciate some help.
    The 3 augmented matrices are in reduced row echelon form. For each state *with a reason* the number of solutions

    \begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}

    \begin{pmatrix}1 & 2 & 0 &1 \\0 & 0 & 1 &2 \\0& 0 &  0&0\end{pmatrix}


    \begin{pmatrix}1 & 0 & 0 &1 \\0 &  1& 0 &2 \\0& 0 &  1& 3\end{pmatrix}
    Last edited by zzizi; May 22nd 2012 at 05:48 AM.
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  2. #2
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    Re: Solutions to these matrices

    Quote Originally Posted by zzizi View Post
    Hi

    This may be basic, but i'd really appreciate some help.
    The 3 augmented matrices are in reduced row echelon form. For each state *with a reason* the number of solutions

    \begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}

    \begin{pmatrix}1 & 2 & 0 &1 \\0 & 0 & 1 &2 \\0& 0 &  0&0\end{pmatrix}


    \begin{pmatrix}1 & 0 & 0 &1 \\0 &  1& 0 &2 \\0& 0 &  1& 3\end{pmatrix}
    Try writing each row as an equation with the variables. The answers should then be obvious...
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  3. #3
    Member zzizi's Avatar
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    Re: Solutions to these matrices

    The soln to this matrix is x1 = 1-2x2
    X3=0
    But is that enough as explanation?
    \begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}
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    Re: Solutions to these matrices

    Quote Originally Posted by zzizi View Post
    The soln to this matrix is x1 = 1-2x2
    X3=0
    But is that enough as explanation?
    \begin{pmatrix}1 &2 & 0 &1 \\0& 0 & 1 & 0 \\0& 0 & 0 & 1\\0& 0 & 0 &0\end{pmatrix}
    Since x_2 is a free variable, wouldn't that mean there are an infinite number of solutions?
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