Find the cofactor of the indicated element.
-$a_{12}$
$\left|\begin{array}{rrr}
-2 & -1 & 0 \
5 & 5 & 2 \
3 & 4 & 5
\end{array}\right|$

A) 10
B) 5
C) $- 19$
D) 19

Question

Find the cofactor of the indicated element.
-$a_{12}$
$\left|\begin{array}{rrr}
-2 & -1 & 0 \
5 & 5 & 2 \
3 & 4 & 5
\end{array}\right|$

A) 10
B) 5
C) $- 19$
D) 19

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 $a_{12}$, which is in the first row and second column, we calculate the minor by removing the first row and second column, leaving us with the matrix:$$\begin{vmatrix}5 & 2 \3 & 5 \\end{vmatrix}$$The determinant of this 2x2 matrix is $5*5 - 2*3 = 25 - 6 = 19$. Since $i+j = 1+2 = 3$, an odd number, we multiply the determinant by $-1$, resulting in $-19$.

Find the Cofactor of the Indicated Element a12a_{12}a12​ ∣−2−10552345∣\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|​−253​−154​025​​

Find the Cofactor of the Indicated Element $a_{12}$ $\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|$