Find the cofactor of the indicated element.
$\begin{array} { l }
\text { a } 33 \
\left| \begin{array} { r r r }
4 & 3 & 2 \
5 & 4 & 2 \
- 1 & - 1 & 4
\end{array} \right|
\end{array}$
A) -1
B) 1
C) -2
D) 2

Question

Find the cofactor of the indicated element.
$\begin{array} { l } 
\text { a } 33 \
\left| \begin{array} { r r r } 
4 & 3 & 2 \
5 & 4 & 2 \
- 1 & - 1 & 4
\end{array} \right|
\end{array}$
A) -1
B) 1
C) -2
D) 2

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 $a_{33}$ (which is the element in the 3rd row and 3rd column, with a value of 4), we first find its minor by removing the 3rd row and 3rd column, leaving us with the matrix:$$\begin{array}{rr}4 & 3 \5 & 4 \\end{array}$$The determinant of this 2x2 matrix is $4*4 - 3*5 = 16 - 15 = 1$.Since $i+j = 3+3 = 6$, and $(-1)^6 = 1$, the cofactor is $1 * 1 = 1$.

Find the Cofactor of the Indicated Element a 33∣432542−1−14∣\begin{array} { l } \text { a } 33 \\\left| \begin{array} { r r r } 4 & 3 & 2 \\5 & 4 & 2 \\- 1 & - 1 & 4\end{array} \right|\end{array} a 33​45−1​34−1​224​​​

Find the Cofactor of the Indicated Element $\begin{array} { l } \text { a } 33 \\\left| \begin{array} { r r r } 4 & 3 & 2 \\5 & 4 & 2 \\- 1 & - 1 & 4\end{array} \right|\end{array}$