Answer
The minors are:
$M_{11}=−5$
$M_{12}=0$
$M_{13}=4$
$M_{21}=47$
$M_{22}=-2$
$M_{23}=-38$
$M_{31}=3$
$M_{32}=0$
$M_{33}=-2$
The cofactors of the matrix A are:
$C_{11}=−5$
$C_{12}=0$
$C_{13}=4$
$C_{21}=-47$
$C_{22}=-2$
$C_{23}=38$
$C_{31}=3$
$C_{32}=0$
$C_{33}=-2$
Work Step by Step
We are given:
$A=\begin{bmatrix}
2 & 10 & 3\\
0 & -1 & 0 \\
4 & 1 & 5
\end{bmatrix}$
The minors are:
$M_{11}=−5$
$M_{12}=0$
$M_{13}=4$
$M_{21}=47$
$M_{22}=-2$
$M_{23}=-38$
$M_{31}=3$
$M_{32}=0$
$M_{33}=-2$
The cofactors of the matrix A are:
$C_{11}=(−1)^{1+1}.4=−5$
$C_{12}=(−1)^{1+2}.2=0$
$C_{13}=(−1)^{1+3}.2=4$
$C_{21}=(−1)^{2+1}.47
=-47$
$C_{22}=(−1)^{2+2}.(-2)=-2$
$C_{23}=(−1)^{2+3}.(-38)=38$
$C_{31}=(−1)^{3+1}.3=3$
$C_{32}=(−1)^{3+2}.0=0$
$C_{33}=(−1)^{3+3}.(-2)=-2$
