Q. The minors of$- 4$ and 9 and the cofactors of$- 4$ and 9 in matrix$\begin{bmatrix} - 1 & - 2 & 3 \\ - 4 & - 5 & - 6 \\ - 7 & 8 & 9 \end{bmatrix}$ are respectively
A) $42,\ 3, - 42,3$
B) $- 42, - 3,\ 42,\ - 3$
C) $42,\ 3,\ - 42,\ - 3$
D) $42,\ 3,\ 42,\ 3$
Explanation
(b)
Minor of ($- 4) = \left| \begin{matrix}
- 2 & 3 \\
8 & 9
\end{matrix} \right| = - 42$
Minor of 9=$\left| \begin{matrix}
- 1 & - 2 \\
- 4 & - 5
\end{matrix} \right| = - 3$
Cofactor of$( - 4) = ( - 1)^{2 + 1}.\ \left| \begin{matrix}
- 2 & 3 \\
8 & 9
\end{matrix} \right| = 42$
and cofactor of $9 = ( - 1)^{3 + 3}.\left| \begin{matrix}
- 1 & - 2 \\
- 4 & - 5
\end{matrix} \right| = - 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.