Find the cofactor of the indicated element.
-
a 12
$$\begin{array} { l }
\left| \begin{array} { r r r }
- 2 & - 1 & 0 \
5 & 5 & 1 \
3 & 4 & 5
\end{array} \right|
\end{array}$$
A) 15
B) 5
C) $- 22$
D) 22

Question

Find the cofactor of the indicated element.
-
a 12 
$$\begin{array} { l } 
\left| \begin{array} { r r r } 
- 2 & - 1 & 0 \
5 & 5 & 1 \
3 & 4 & 5
\end{array} \right|
\end{array}$$
A) 15
B) 5
C) $- 22$
D) 22

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 indices of the element, respectively. For the element $a_{12}$ (which is $-1$), located in the first row and second column ($i=1$, $j=2$), we remove the first row and second column to find its minor:$$\begin{vmatrix}5 & 1 \3 & 5\end{vmatrix}= (5*5) - (1*3) = 25 - 3 = 22$$Then, the cofactor is $(-1)^{1+2} \times 22 = -22$.

Find the Cofactor of the Indicated Element ∣−2−10551345∣\begin{array} { l } \left| \begin{array} { r r r } - 2 & - 1 & 0 \\5 & 5 & 1 \\3 & 4 & 5\end{array} \right|\end{array}​−253​−154​015​​​

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