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)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & - 24 \ - 3 & - 18 \end{array} \right| = 90$
$C _ { 13 } = - 90$

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

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)
$M _ { 13 } = \left| \begin{array} { c c } - 9 & - 24 \ - 3 & - 18 \end{array} \right| = 90$
$C _ { 13 } = - 90$

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

Quizplus · Accepted Answer

The minor $M_{13}$ is found by deleting the first row and third column, resulting in a determinant of the 2x2 matrix formed by the remaining elements. The calculation gives $63$. The cofactor $C_{13}$ is $M_{13}$ times $(-1)^{1+3}$, which equals $63$.

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

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