$$ A \text{ matrix } A = \begin{bmatrix} 2 & 5 \\ -11 & 7 \end{bmatrix}, \quad (\operatorname{adj} A) \text{ is equal to } $$
Solution
Explaination
To find the adjoint of the matrix $$ A = \begin{bmatrix} 2 & 5 \\ -11 & 7 \end{bmatrix} $$ and then its transpose, we follow these steps: Step 1: Cofactors $$ C_{ij} = (-1)^{i+j} M_{ij} $$ Step 2: Cofactor Matrix $$ C = \begin{bmatrix} 7 & 11 \\ -5 & 2 \end{bmatrix} $$ Step 3: Adjoint of A $$ \operatorname{adj}(A) = C^T = \begin{bmatrix} 7 & -5 \\ 11 & 2 \end{bmatrix} $$ Step 4: Transpose of the Adjoint $$ \operatorname{adj}(A)^T = \begin{bmatrix} 7 & 11 \\ -5 & 2 \end{bmatrix} $$ Final Answer $$ \begin{bmatrix} 7 & 11 \\ -5 & 2 \end{bmatrix} $$