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Math Help - Matrix doing a cofactor expansion

  1. #1
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    Question Matrix doing a cofactor expansion

    Evaluate the determinant of the following matrix A =
    <br />
\left|\begin{array}{ccccc}2 & 1 & -3 & -1 & 2 \\ 0 & -1 & 0 & 3 & 1 \\ 0 & 2 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 3 & 0 & 3 & 2 \end{array}\right|<br />

    by doing a co-factor expansion.

    Please expalin how to do it, thank you!
    this is the exercise on my task
    Last edited by lin.13579; September 2nd 2009 at 05:39 PM.
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  2. #2
    Member eXist's Avatar
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    If you have:

    \begin{array}{lcr}<br />
\mbox a & b & c \\<br />
\mbox d & e & f \\<br />
\mbox g & h & i\end{array}<br />

    The cofactor for a is the determinant of:

    \begin{array}{lcr}<br />
\mbox e & f \\<br />
\mbox h & i \end{array}<br />

    The cofactor for b is negative(-) of the determinant of:

    \begin{array}{lcr}<br />
\mbox d & f \\<br />
\mbox g & i \end{array}<br />

    The cofactor for c is the determinant of:

    \begin{array}{lcr}<br />
\mbox d & e \\<br />
\mbox g & h \end{array}<br />
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  3. #3
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    Why are you being asked to do a "co-factor expansion" if you don't know what that is?

    I would recommend starting your co-factor expansion using the first column. That way you just have 2 times \left|\begin{array}{cccc}-1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2\end{array}\right| and expand that determinant on the second column. Do you see why?
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Why are you being asked to do a "co-factor expansion" if you don't know what that is?

    I would recommend starting your co-factor expansion using the first column. That way you just have 2 times \left|\begin{array}{cccc}-1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2\end{array}\right| and expand that determinant on the second column. Do you see why?
    I am sorry, I am not good on maths , can you explain more please !!!
    I don't understand what is "just have 2 times" mean?
    Is it mean 2 times every number 1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2 to evaluate matrix A?
    Last edited by lin.13579; September 2nd 2009 at 05:42 PM.
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