Find the cofactor of the indicated element.
-$\text { a11 }$
$\left|\begin{array}{rrr}
-1 & 0 & 2 \
2 & 2 & 4 \
2 & 5 & 1
\end{array}\right|$

A) 6
B) 18
C) $- 18$
D) $- 2$

Question

Find the cofactor of the indicated element.
-$\text { a11 }$
$\left|\begin{array}{rrr}
-1 & 0 & 2 \
2 & 2 & 4 \
2 & 5 & 1
\end{array}\right|$

A) 6
B) 18
C) $- 18$
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 element $a_{11}$, which is $-1$, the minor is obtained by deleting the row and column of $a_{11}$, resulting in the determinant of the $2 \times 2$ matrix $\left|\begin{array}{cc} 2 & 4 \ 5 & 1 \end{array}\right|$. The determinant of this matrix is $2(1) - 4(5) = 2 - 20 = -18$. Since $i+j = 1+1 = 2$, and $(-1)^2 = 1$, the cofactor is $1 \times -18 = -18$.

Find the Cofactor of the Indicated Element a11 \text { a11 } a11

Find the Cofactor of the Indicated Element $\text { a11 }$