Question

The matrix [5103−2−46−1−2b]is a singular matrix, if b equals

• A. -3
• B. 3
• C. 0
• D. any value

Answer 1

Answer: (D)

any value

Answer 2

Explanation:
The matrix $\begin{bmatrix} 5 & 10 & 3 \\\ -2 & -4 & -6 \\\ -1 & -2 & b \end{bmatrix}$ is singular, if $\begin{vmatrix} 5 & 10 & 3\\\ -2 & -4 & 6\\\ -1 & -2 & b \end{vmatrix} = 0$
⇒ The given matrix is singular for any
⇒ −1(60+12) + 2(30+6) + b(−20+20) = 0
⇒ −72 + 72 + 0b = 0
⇒ 0 = 0

Therefore, there is no specific value.