If A = begin{bmatrix} a & 1 & 2 1 & 2 & b c | vedclass

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(A) We know that $\operatorname{Adj} A = \begin{bmatrix} C_{11} & C_{21} & C_{31} \ C_{12} & C_{22} & C_{32} \ C_{13} & C_{23} & C_{33} \end{bmatrix

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$10$

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(A) We know that $\operatorname{Adj} A = \begin{bmatrix} C_{11} & C_{21} & C_{31} \ C_{12} & C_{22} & C_{32} \ C_{13} & C_{23} & C_{33} \end{bmatrix}$,where $C_{ij}$ is the cofactor of the element $a_{ij}$.Given $\operatorname{Adj} A = \begin{bmatrix} 7 & -1 & -5 \ -3 & 9 & 5 \ 1 & -3 & 5 \end{bmatrix}$.Comparing the elements:$C_{11} = 7 \Rightarrow \begin{vmatrix} 2 & b \ 1 & 3 \end{vmatrix} = 7 \Rightarrow 6 - b = 7 \Rightarrow b = -1$.$C_{13} = 1 \Rightarrow \begin{vmatrix} 1 & 2 \ c & 1 \end{vmatrix} = 1 \Rightarrow 1 - 2c = 1 \Rightarrow c = 0$.$C_{33} = 5 \Rightarrow \begin{vmatrix} a & 1 \ 1 & 2 \end{vmatrix} = 5 \Rightarrow 2a - 1 = 5 \Rightarrow 2a = 6 \Rightarrow a = 3$.Thus,$a^2 + b^2 + c^2 = (3)^2 + (-1)^2 + (0)^2 = 9 + 1 + 0 = 10$.

If $A = \begin{bmatrix} a & 1 & 2 \\ 1 & 2 & b \\ c & 1 & 3 \end{bmatrix}$ and $\operatorname{Adj} A = \begin{bmatrix} 7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5 \end{bmatrix}$,then $a^2 + b^2 + c^2 = $

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