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Math Help - Another matrix as elementary matrices

  1. #1
    Junior Member
    Joined
    Jan 2010
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    Another matrix as elementary matrices

    Hey everyone

    I am trying to write this matrix as a product elementary matrices:

    <br />
\begin{bmatrix}<br />
-3 & 1 \\ <br />
2 & 2<br />
\end{bmatrix}<br />

    I keep on getting this answer:
    <br />
\begin{bmatrix}<br />
-3 & 0 \\ <br />
0 & 1<br />
\end{bmatrix}<br /> <br />
\begin{bmatrix}<br />
1 & 0 \\ <br />
2 & 1<br />
\end{bmatrix}<br /> <br />
\begin{bmatrix}<br />
1 & 0 \\ <br />
0 & \frac4{3}<br />
\end{bmatrix}<br /> <br />
\begin{bmatrix}<br />
1 & -\frac{1}3 \\ <br />
0 & 1<br />
\end{bmatrix}<br />

    I've did it 3 times and keep getting the same answer. Can someone point me to where I am going wrong.

    Thanks
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Can this system be solved?

    \displaystyle \begin{bmatrix}<br />
-3 & 0 \\<br />
0 & 1<br />
\end{bmatrix}<br /> <br />
\begin{bmatrix}<br />
l_{11} & 0 \\<br />
l_{21} & l_{22}<br />
\end{bmatrix}<br />
\times <br />
\begin{bmatrix}<br />
u_{11} & u_{12} \\<br />
0 &  u_{22}<br />
\end{bmatrix}

    \displaystyle -3=l_{11}u_{11}

    \displaystyle 1= l_{11}u_{12}

    \displaystyle 2=l_{21}u_{11}

    \displaystyle 2=l_{21}u_{12}+l_{12}u_{22}
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  3. #3
    MHF Contributor
    Joined
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    Florida
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    Quote Originally Posted by pickslides View Post
    Can this system be solved?

    \displaystyle \begin{bmatrix}<br />
-3 & 0 \\<br />
0 & 1<br />
\end{bmatrix}<br /> <br />
\begin{bmatrix}<br />
l_{11} & 0 \\<br />
l_{21} & l_{22}<br />
\end{bmatrix}<br />
\times <br />
\begin{bmatrix}<br />
u_{11} & u_{12} \\<br />
0 &  u_{22}<br />
\end{bmatrix}

    \displaystyle -3=l_{11}u_{11}

    \displaystyle 1= l_{11}u_{12}

    \displaystyle 2=l_{21}u_{11}

    \displaystyle 2=l_{21}u_{12}+l_{12}u_{22}
    This the LU Factorization which I informed you of yesterday evant8950.

    pickslides, did you mean to write this

    \displaystyle \begin{bmatrix}<br />
-3 & 1 \\<br />
2 & 2<br />
\end{bmatrix}=<br /> <br />
\begin{bmatrix}<br />
l_{11} & 0 \\<br />
l_{21} & l_{22}<br />
\end{bmatrix}<br />
\times <br />
\begin{bmatrix}<br />
u_{11} & u_{12} \\<br />
0 &  u_{22}<br />
\end{bmatrix}\text{?}
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