Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } - 3 & 2 & - 8 \ 3 & - 2 & 6 \ - 1 & 3 & - 6 \end{array} \right]$.
A)
$M _ { 13 } = \left| \begin{array} { c c } - 3 & - 8 \ - 1 & - 6 \end{array} \right| = 10$
$C _ { 13 } = - 10$

B)
$M _ { 13 } = \left| \begin{array} { c c } 2 & - 8 \ - 2 & 6 \end{array} \right| = - 4$
$C _ { 13 } = - 4$

C)
$M _ { 13 } = \left| \begin{array} { c c } 3 & - 2 \ - 1 & 3 \end{array} \right| = 7$
$C _ { 13 } = - 7$

D)
$M _ { 13 } = \left| \begin{array} { c c } 2 & - 8 \ - 2 & 6 \end{array} \right| = - 4$
$C _ { 13 } = 4$

E)
$$\begin{array} { l }
M _ { 13 } = \left| \begin{array} { c c }
3 & - 2 \
- 1 & 3
\end{array} \right| = 7 \
C _ { 13 } = 7
\end{array}$$

Question

Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } - 3 & 2 & - 8 \ 3 & - 2 & 6 \ - 1 & 3 & - 6 \end{array} \right]$.
A)
$M _ { 13 } = \left| \begin{array} { c c } - 3 & - 8 \ - 1 & - 6 \end{array} \right| = 10$
$C _ { 13 } = - 10$

B)
$M _ { 13 } = \left| \begin{array} { c c } 2 & - 8 \ - 2 & 6 \end{array} \right| = - 4$
$C _ { 13 } = - 4$

C)
$M _ { 13 } = \left| \begin{array} { c c } 3 & - 2 \ - 1 & 3 \end{array} \right| = 7$
$C _ { 13 } = - 7$

D)
$M _ { 13 } = \left| \begin{array} { c c } 2 & - 8 \ - 2 & 6 \end{array} \right| = - 4$
$C _ { 13 } = 4$

E)
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
3 & - 2 \
- 1 & 3
\end{array} \right| = 7 \
C _ { 13 } = 7
\end{array}$$

Quizplus · Accepted Answer

To find the minor $M_{13}$, we remove the first row and third column of the matrix, leaving us with a $2 \times 2$ matrix. The determinant of this matrix gives us the minor. For the cofactor $C_{13}$, we apply $(-1)^{1+3}$ to the minor. Since $1+3=4$ is even, the sign doesn't change, so the cofactor is the same as the minor in this case.

Find the Minor M13M _ { 13 }M13​ And Its Cofactor C13C _ { 13 }C13​

Find the Minor $M _ { 13 }$ And Its Cofactor $C _ { 13 }$