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) $\quad M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = - 36$

C)
$\begin{array}{l}
M_{13}=\left|\begin{array}{cc}
-9 & 6 \
3 & -9
\end{array}\right|=63 \
C_{13}=-63
\end{array}$

D)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = 36$

E)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right| = 63$
$$C _ { 13 } = 63$$

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) $\quad M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = - 36$

C)
$\begin{array}{l}
M_{13}=\left|\begin{array}{cc}
-9 & 6 \
3 & -9
\end{array}\right|=63 \
C_{13}=-63
\end{array}$

D)
$M _ { 13 } = \left| \begin{array} { c c } - 6 & 24 \ 6 & - 18 \end{array} \right| = - 36$
$C _ { 13 } = 36$

E)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right| = 63$
$$C _ { 13 } = 63$$

Quizplus · Accepted Answer

The minor $M_{13}$ is found by deleting the first row and third column of the matrix, resulting in $\left| \begin{array} { c c } - 9 & 6 \ 3 & - 9 \end{array} \right|$, which equals 63. The cofactor $C_{13}$ is $M_{13}$ times $(-1)^{1+3}$, which equals 63 since the exponent is even, making the sign positive.

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

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