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Find the cofactor of \( a_{12}\) in the following \[ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}\]

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  • Cofactor of an element [$a_{ij}]$ is [A$_{ij}]$ which is obtained by $(-1)^{i+j}.M_{ij}$
Given $A=\begin{vmatrix}2 & -3 & 5\\6 & 0 & 4\\1 & 5 & -7\end{vmatrix}$
 
The cofactor of $a_{12}$ is
 
$M_{12}=\begin{vmatrix}6 & 4\\1 & -7\end{vmatrix}$=-42-4=-46.
 
$[A_{12}]=(-1)^{1+2}.(-46)=46.$
 
Hence The cofactor of $A_{12}$ is 46.

 

answered Mar 11, 2013 by sreemathi.v
 

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