Find the cofactor of the indicated element.
-$a _ { 13 }$
$$\left| \begin{array} { r r r }
- 2 & - 1 & 0 \
1 & 2 & 3 \
4 & 4 & 2
\end{array} \right|$$
A) $- 4$
B) $- 10$
C) 4
D) $- 8$

Question

Find the cofactor of the indicated element.
-$a _ { 13 }$
$$\left| \begin{array} { r r r } 
- 2 & - 1 & 0 \
1 & 2 & 3 \
4 & 4 & 2
\end{array} \right|$$
A) $- 4$
B) $- 10$
C) 4
D) $- 8$

Quizplus · Accepted Answer

The cofactor of an element in a matrix is calculated by multiplying the minor of that element by $(-1)^{i+j}$, where $i$ and $j$ are the row and column numbers of the element, respectively. For $a_{13}$, $i=1$ and $j=3$, so we calculate the minor by removing the first row and third column, leaving us with the 2x2 matrix:$$\begin{pmatrix} 1 & 2 \ 4 & 4 \end{pmatrix}$$The determinant of this matrix is $1(4) - 2(4) = 4 - 8 = -4$. Thus, the cofactor of $a_{13}$ is $(-1)^{1+3}(-4) = (-1)^4(-4) = -4$.

Find the Cofactor of the Indicated Element a13a _ { 13 }a13​

Find the Cofactor of the Indicated Element $a _ { 13 }$