Q. The matrix $\begin{bmatrix} 5 & 10 & 3 \\ - 2 & - 4 & 6 \\ - 1 & - 2 & b \end{bmatrix}$ is a singular matrix, if $b$ is equal to
A) $- 3$
B) 3
C) 0
D) For any value of $b$
Explanation
(d)
Since, the given matrix is singular.
$\therefore\begin{bmatrix}
5 & 10 & 3 \\
- 2 & - 4 & 6 \\
- 1 & - 2 & b
\end{bmatrix} = 0$
$\Rightarrow 5( - 4b + 12) - 10( - 2b + 6) + 3(4 - 4) = 0$
$\Rightarrow \ \ - 20b + 60 + 20b - 60 = 0$
$\Rightarrow \ \ 0(b) = 0$
$\therefore The\$given matrix is singular for any value of $b$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.