Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } 9 & - 6 & 24 \ - 9 & 6 & - 18 \ 3 & - 9 & 18 \end{array} \right]$.
A) $M _ { 13 } = \left| \begin{array} { l l } 9 & 24 \ 3 & 18 \end{array} \right| = 90$
$C _ { 13 } = - 90$
B)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = - 36$
C)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right| = 63$
$C _ { 13 } = - 63$
D)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = 36$
E)
$$\begin{array} { l }
M _ { 13 } = \left| \begin{array} { c c }
- 9 & 6 \
3 & - 9
\end{array} \right| = 63 \
C _ { 13 } = 63
\end{array}$$

Question

Find the minor $M _ { 13 }$ and its cofactor $C _ { 13 }$ of the matrix $\left[ \begin{array} { c c c } 9 & - 6 & 24 \ - 9 & 6 & - 18 \ 3 & - 9 & 18 \end{array} \right]$.
A) $M _ { 13 } = \left| \begin{array} { l l } 9 & 24 \ 3 & 18 \end{array} \right| = 90$
$C _ { 13 } = - 90$
B)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = - 36$
C)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right| = 63$
$C _ { 13 } = - 63$
D)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = 36$
E)
$$\begin{array} { l } 
M _ { 13 } = \left| \begin{array} { c c } 
- 9 & 6 \
3 & - 9
\end{array} \right| = 63 \
C _ { 13 } = 63
\end{array}$$

Quizplus · Accepted Answer

To find the minor $M_{13}$, we remove the first row and third column of the matrix, leaving us with the matrix $\left[ \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right]$. The determinant of this matrix is $ (-9) \times (-9) - (6) \times (3) = 81 - 18 = 63$, so $M_{13} = 63$. The cofactor $C_{13}$ is given by $(-1)^{1+3} \times M_{13} = (-1)^4 \times 63 = 63$, hence the correct answer is E.

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

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