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Question: If the matrix A= \(\begin{bmatrix} 8 & –6 & 2 \\ –6 & 7 & –4 \\ 2 & –4 & \lambda \end{bmatrix}\) is ...

If the matrix A= [8–62–67–42–4λ]\begin{bmatrix} 8 & –6 & 2 \\ –6 & 7 & –4 \\ 2 & –4 & \lambda \end{bmatrix} is singular, then l equal to–

A

– 5

B

1

C

3

D

–1

Answer

3

Explanation

Solution

A = Singular ̃ |A| = 0

∣8–62–67–42–4λ∣\left| \begin{matrix} 8 & –6 & 2 \\ –6 & 7 & –4 \\ 2 & –4 & \lambda \end{matrix} \right| = 0

̃ 8(7l – 16) + 6(– 6l + 8) + 2(24 – 14) = 0

̃ 56l –128 –36l + 48 + 20 = 0

̃ 20l = 60 ̃ l = 3