Find the cofactor of the indicated element.
-$\text { a33 }$
$\left|\begin{array}{rrr}
3 & 3 & 2 \
3 & 5 & 4 \
-1 & -1 & 4
\end{array}\right|$

A) 6
B) $- 2$
C) 2
D) $- 6$

Question

Find the cofactor of the indicated element.
-$\text { a33 }$
$\left|\begin{array}{rrr}
3 & 3 & 2 \
3 & 5 & 4 \
-1 & -1 & 4
\end{array}\right|$

A) 6
B) $- 2$
C) 2
D) $- 6$

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 in the 3rd row and 3rd column, we first find the minor by deleting the 3rd row and 3rd column, leaving us with the submatrix:$$\begin{pmatrix}3 & 3 \3 & 5 \\end{pmatrix}$$The determinant of this submatrix is $3*5 - 3*3 = 15 - 9 = 6$. Since $i+j = 3+3 = 6$, which is even, the cofactor is $6$.

Find the Cofactor of the Indicated Element a33 \text { a33 } a33

Find the Cofactor of the Indicated Element $\text { a33 }$