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Math Help - Find the determminant?

  1. #1
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    Find the determminant?

    find the determinant
    0 1 -2
    -2 2 0
    -3 4 1


    find the inverse
    4 -5
    1 -1


    find the deterinant
    -4 3
    5 0
    Last edited by mr fantastic; December 13th 2010 at 06:17 PM. Reason: Title.
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  2. #2
    MHF Contributor
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    I expanded across the first row.

    \displaystyle <br />
\begin{vmatrix}<br />
0 & 1 & -2\\ <br />
-2 & 2 & 0\\ <br />
-3 & 4 & 1<br />
\end{vmatrix}\Rightarrow 0*\begin{vmatrix}<br />
2 & 0  \\ <br />
4 &  1<br />
\end{vmatrix}-1*\begin{vmatrix}<br />
-2 & 0  \\ <br />
-3 &  1<br />
\end{vmatrix}-2*\begin{vmatrix}<br />
-2 & 2  \\ <br />
-3 & 4<br />
\end{vmatrix}=0-1*(-2-0)-2*(-8-(-6))=0+2+4=6

    You should be able to do this one by using 1 and 3 as an outline.

    \displaystyle A^{-1}=\frac{1}{det(A)}*A

    \displaystyle\begin{vmatrix}<br />
-4 & 3  \\ <br />
5 & 0<br />
\end{vmatrix}=-4*0-5*3=0-15=-15

    Definition:
    The determinant of an n x n matrix A is defined as

    \displaystyle <br />
det(A) =<br />
\begin{cases}<br />
 a_{11}, & \mbox{if } \ n=1 \\<br />
 a_{11}A_{11}+a_{12}A_{12}+\dots +a_{1n}A_{1n}, & \mbox{if } \ n>1<br />
\end{cases}<br />

    where

    \displaystyle A_{1j}=(-1)^{1+j}det(M_{1j}) \ j=1,2,\cdots , n

    are the cofactors associated with the first row expansion.
    Last edited by dwsmith; December 13th 2010 at 03:50 PM.
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