A) \[\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2 & -1 \\ -7 & 4 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -2 & 7 \\ 1 & -4 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -2 & 1 \\ 7 & -4 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Let\[A=\left[ \begin{matrix} 4 & 7 \\ 1 & 2 \\ \end{matrix} \right]\] \[|A|=8-7=1\] Cofactors of \[A\] are \[{{C}_{11}}=2,\,\,{{C}_{12}}=-1\] \[{{C}_{21}}=-7,\,\,{{C}_{22}}=4\] \[\therefore \] \[adj\,\,(A)=\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\] \[\therefore \] \[{{A}^{-1}}=\frac{adj\,\,(A)}{|A|}=\frac{1}{1}\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\] Note: If a matrix,\[A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\], then \[adj\,\,(A)=\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right]\].
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