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  4. Find the cofactors of the element of third row and second column of the following determinant | beginmatrix1&x&y+z 1&y&z+x 1&z&x+y endmatrix|⋅

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Q. Find the cofactors of the element of third row and second column of the following determinant
$\left|\begin{matrix}1&x&y+z\\ 1&y&z+x\\ 1&z&x+y\end{matrix}\right|\cdot$

Determinants

Solution:

$M_{32}=\left|\begin{matrix}1&y+z\\ 1&z+x\end{matrix}\right|=z+x-y-z=x-y$
$\Rightarrow \quad c_{32}=-M_{32}=y-x$