Find the cofactor of the given element.
-$$\begin{array} { l }
a _ { 13 } \
A = \left[ a _ { i j } \right] = \left[ \begin{array} { r r r }
7 & - 2 & 5 \
2 & 5 & 4 \
- 1 & - 9 & 3
\end{array} \right]
\end{array}$$
A) $- 8$
B) $- 18$
C) 13
D) $- 13$

Question

Find the cofactor of the given element.
-$$\begin{array} { l } 
a _ { 13 } \
A = \left[ a _ { i j } \right] = \left[ \begin{array} { r r r } 
7 & - 2 & 5 \
2 & 5 & 4 \
- 1 & - 9 & 3
\end{array} \right]
\end{array}$$
A) $- 8$
B) $- 18$
C) 13
D) $- 13$

Quizplus · Accepted Answer

The cofactor of an element $a_{ij}$ in a matrix is given by $C_{ij} = (-1)^{i+j}M_{ij}$, where $M_{ij}$ is the determinant of the matrix obtained by deleting the $i$th row and $j$th column. For $a_{13}$, $i=1$ and $j=3$, so we delete the first row and third column, leaving us with the submatrix $\left[ \begin{array}{rr} 2 & 5 \ -1 & -9 \end{array} \right]$. The determinant of this submatrix is $(2)(-9) - (5)(-1) = -18 + 5 = -13$. Thus, the cofactor $C_{13} = (-1)^{1+3}(-13) = (-1)^4(-13) = -13$.

Find the Cofactor of the Given Element A) −8- 8−8 B) −18- 18−18

Find the Cofactor of the Given Element A) $- 8$ B) $- 18$