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Question: If the matrix \(\begin{bmatrix} 1 & 3 & \alpha + 2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix}\) is sin...

If the matrix [13α+22483510]\begin{bmatrix} 1 & 3 & \alpha + 2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{bmatrix} is singular, then a =

A

– 4

B

4

C

2

D

– 2

Answer

4

Explanation

Solution

|A| = 0

∣13α+22483510∣\left| \begin{matrix} 1 & 3 & \alpha + 2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \end{matrix} \right|= 0

1(0) –3 (20–24) + (a + 2) (–2) = 0

12 – 2a – 4 = 0 Ž a = 4