Find λ so that the matrix \(\begin{pmatrix}8 & 9 & 7 \\7 & 8 & 6 \\9

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

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

Answer»

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