Find λ so that the matrix ((8, 9, 7)(7, 8, 6)(9, 10, λ)) is a singular matrix

Question

Find λ so that the matrix \(\begin{pmatrix} 8 & 9 & 7 \\ 7 & 8 & 6 \\ 9 & 10 & λ \end{pmatrix}\) is a singular matrix 

Answer 1

Let A = \(\begin{pmatrix} 8 & 9 & 7 \\ 7 & 8 & 6 \\ 9 & 10 & λ \end{pmatrix}\)

Given A is singular matrix ⇒ |A| = 0

\(\begin{vmatrix} 8 & 9 & 7 \\ 7 & 8 & 6 \\ 9 & 10 & λ \end{vmatrix}\) = 0

8 (8λ - 60) - 9(7λ - 54) + 7(70 - 72) = 0

64λ - 480 - 63λ + 486 - 14 = 0

λ + 6 - 14 = 0 ⇒ λ = 8