# Find the co-factor of $$a_{13}$$ in the following : $\begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}$

Toolbox:
• Co-factor of $[a_{ij}]=(-1)^{i+j}$ times $M_{ij}$.
• Where i is the row and j is the column .
Step 1:
Cofactor of $a_{13}=(-1)^{1+3}(a_{21}\times a_{32}-a_{22}\times a_{31})$
Here $a_{21}=6,a_{32}=5,a_{22}=0,a_{31}=1.$
Co-factor of $a_{13}=(6\times 5-0\times 1)$
$\qquad\qquad\qquad=30-0$
$\qquad\qquad\qquad=30.$