Find the cofactor of the indicated element.
-
$a_{22}$

$$\begin{array} { l }
\left| \begin{array} { r r r }
4 & 1 & 1 \
- 2 & - 1 & 1 \
3 & 1 & 4
\end{array} \right|
\end{array}$$
A) $- 1$
B) 1
C) $- 13$
D) 13

Question

Find the cofactor of the indicated element.
-
$a_{22}$

$$\begin{array} { l } 
\left| \begin{array} { r r r } 
4 & 1 & 1 \
- 2 & - 1 & 1 \
3 & 1 & 4
\end{array} \right|
\end{array}$$
A) $- 1$
B) 1
C) $- 13$
D) 13

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 the element $a_{22}$ (which is $-1$), the minor is obtained by deleting the row and column that $a_{22}$ is in, leaving us with the matrix $\begin{pmatrix} 4 & 1 \ 3 & 4 \end{pmatrix}$. The determinant of this 2x2 matrix is $4*4 - 1*3 = 16 - 3 = 13$. Since $i+j = 2+2 = 4$, and $(-1)^4 = 1$, the cofactor is $1*13 = 13$.

Find the Cofactor of the Indicated Element a22a_{22}a22​ ∣411−2−11314∣\begin{array} { l } \left| \begin{array} { r r r } 4 & 1 & 1 \\- 2 & - 1 & 1 \\3 & 1 & 4\end{array} \right|\end{array}​4−23​1−11​114​​​

Find the Cofactor of the Indicated Element $a_{22}$ $\begin{array} { l } \left| \begin{array} { r r r } 4 & 1 & 1 \\- 2 & - 1 & 1 \\3 & 1 & 4\end{array} \right|\end{array}$