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Determinants

Example 12

Find adj A for \(A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}\)

Solution

We have \(A_{11} = 4, A_{12} = -1, A_{21} = -3, A_{22} = 2\) Hence \(adj A = \begin{bmatrix} A_{11} & A_{21} \\ A_{12} & A_{22} \end{bmatrix} = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}\)