Find the cofactor of the indicated element.
-$a_{11}$
$\left|\begin{array}{rrr}
-1 & 0 & 2 \
3 & 3 & 1 \
4 & 5 & 3
\end{array}\right|$

A) $- 4$
B) 4
C) 12
D) $- 3$

Question

Find the cofactor of the indicated element.
-$a_{11}$
$\left|\begin{array}{rrr}
-1 & 0 & 2 \
3 & 3 & 1 \
4 & 5 & 3
\end{array}\right|$

A) $- 4$
B) 4
C) 12
D) $- 3$

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 $a_{11}$ (which is -1), its minor is obtained by deleting the row and column that $a_{11}$ is in, resulting in the determinant of the 2x2 matrix $\left|\begin{array}{cc} 3 & 1 \ 5 & 3 \end{array}\right|$. The determinant of this matrix is $3*3 - 1*5 = 9 - 5 = 4$. Since $i+j = 1+1 = 2$, the cofactor is $4 * (-1)^2 = 4$.

Find the Cofactor of the Indicated Element a11a_{11}a11​ ∣−102331453∣\left|\begin{array}{rrr}-1 & 0 & 2 \\3 & 3 & 1 \\4 & 5 & 3\end{array}\right|​−134​035​213​​

Find the Cofactor of the Indicated Element $a_{11}$ $\left|\begin{array}{rrr}-1 & 0 & 2 \\3 & 3 & 1 \\4 & 5 & 3\end{array}\right|$