A) \[\left[ \begin{matrix} 10 & 3 \\ 3 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 10 & -3 \\ -3 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -1 & -3 \\ -3 & 10 \\ \end{matrix} \right]\]
Correct Answer: B
Solution :
We have \[A=\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right]\] Cofactors of A are \[{{C}_{11}}=10,{{C}_{12}}=-3\] \[{{C}_{21}}=-3,{{C}_{22}}=1\] \[\text{adj}\,\text{A}={{\left[ \begin{matrix} 10 & -3 \\ -3 & 1 \\ \end{matrix} \right]}^{T}}\] \[=\left[ \begin{matrix} 10 & -3 \\ -3 & 1 \\ \end{matrix} \right]\] Note: If a matrix \[A=\left[ \,\begin{matrix} a & b \\ c & d \\ \end{matrix} \right],\]then \[\text{adj}\,\text{A}=\left[ \begin{matrix} d & -d \\ -c & a \\ \end{matrix} \right]\]
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