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Math Help - Finding Elementary Matrix

  1. #1
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    Finding Elementary Matrix

    I have a problem I need help with. I have the following Matrix A:


    <br />
\begin{array}{ccccc}<br />
6 & 4 & -1 & 2 & 5\\<br />
3 & 0 & -1 & 2 & 7 \\<br />
18 & 3 & 4 & -2 & 0 \\<br />
6 & 8 & 0 & 0 & -4 <br />
\end{array}

    I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

    I have no idea where to start, and I can't find a good reference source.
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  2. #2
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    Quote Originally Posted by notgod View Post
    I have a problem I need help with. I have the following Matrix A:


    <br />
\begin{array}{ccccc}<br />
6 & 4 & -1 & 2 & 5\\<br />
3 & 0 & -1 & 2 & 7 \\<br />
18 & 3 & 4 & -2 & 0 \\<br />
6 & 8 & 0 & 0 & -4 <br />
\end{array}

    I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

    I have no idea where to start, and I can't find a good reference source.
    This is easier than it seems. Elementary matrices are just matrices that result from elementary matrix operations. For this problem, look at columns 4 and 2. Can you find 2*C_4? I bet so. What about C_2-2*C_4? I bet so.

    Now the new matrix will be the starting one with column 2 being changed to the answer from above.
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  3. #3
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    Quote Originally Posted by notgod View Post
    I have a problem I need help with. I have the following Matrix A:


    <br />
\begin{array}{ccccc}<br />
6 & 4 & -1 & 2 & 5\\<br />
3 & 0 & -1 & 2 & 7 \\<br />
18 & 3 & 4 & -2 & 0 \\<br />
6 & 8 & 0 & 0 & -4 <br />
\end{array}

    I need to find an elementary matrix with subtracts 2 times column 4 from column 2 of matrix A.

    I have no idea where to start, and I can't find a good reference source.
    I think you are confusing terminology. An "elementary matrix" doesn't depend on a "matrix A". If you are looking for an elementary matrix that "subtracts 2 times column 4 from column 2" of any matrix it multiplies, just set up the 5 by 5 identity matrix and subtract two times column 4 from column 2 of it. That is, all except column 2 will be unchanged and it will just have a "-2" in the 4th row, in addition to the "1" in the second row.
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