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प्रश्न
Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:
\[A = \begin{bmatrix}- 1 & 4 \\ 2 & 3\end{bmatrix}\]
उत्तर
\[M_{11} = 3\]
\[ M_{21} = 4\]
\[ C_{ij} = \left( - 1 \right)^{i + j} M_{ij} \]
\[ C_{11} = \left( - 1 \right)^{1 + 1} M_{11} = 3\]
\[ C_{21} = \left( - 1 \right)^{2 + 1} M_{21} = - \left( 4 \right) = - 4\]
\[D = \left( 3 \times - 1 \right) - \left( 4 \times 2 \right) = - 3 - 8 = - 11\]
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