Question

The matrix $\left[\begin{array}{ccc}5& 10& 3\\ -2& -4& 6\\ -1& -2& b\end{array}\right]$is a singular matrix, if b equals

• A. -3
• B. 3
• C. 0
• D. any value

Answer 1

The Correct Option is D

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.