Question

Write the cofactor of a₁₂ in the following matrix \[\begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix} .\]

Answer 1

\[\text{ Given: }\begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix}\] 
Here, 
\[ a_{12} = - 3\] 
\[\text{ Cofactor of }a_{12} = \left( - 1 \right)^{1 + 2} \begin{vmatrix}6 & 4 \\ 1 & - 7\end{vmatrix} = - ( - 42 - 4) = 46\]