Find the adjoint of the following matrices : [ cc 2 & -3 3 & 5 ] - Vidyadip

Question

Find the adjoint of the following matrices : $\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$

✓

Answer

$
A=\left[\begin{array}{rr}
2 & -3 \\
3 & 5
\end{array}\right]
$
Here, $a_{11}=2, M _{11}=5$
$
\begin{aligned}
& \therefore A _{11}=(-1)^{1+1}(5)=5 \\
& a_{12}=-3, M _{12}=3 \\
& \therefore A _{12}=(-1)^{1+2}(3)=-3
\end{aligned}
$
$
\begin{aligned}
& a_{21}=3, M _{21}=-3 \\
& \therefore A _{21}=(-1)^{2+1}(-3)=3 \\
& a_{22}=5, M _{22}=2 \\
& \therefore A _{22}=(-1)^{2+2}=2
\end{aligned}
$
$\therefore$ the cofactor matrix $=\left(\begin{array}{ll} A _{11} & A _{12} \\ A _{21} & A _{22}\end{array}\right]=\left[\begin{array}{rr}5 & -3 \\ 3 & 2\end{array}\right)$
$\therefore \operatorname{adj} A=\left[\begin{array}{rr}5 & 3 \\ -3 & 2\end{array}\right] \cdot$

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