Subject: Applied Mathematics 2

Topic: Matrices

Difficulty: Low

To find eigen values of A ,characteristic eqation is |A- λI| =0

i.e. $ \begin{vmatrix} 2-λ&0&-1 \\ 0&2-λ&0 \\ -1&0&2-λ \end{vmatrix} = 0 $

Expanding we get a cubic equation in λ as $λ^3 - 6λ^2 + 11λ - 6 =0$ i.e. λ = 1, 2, 3

If λ is the eigen value of A ,then by the property eigen values of $adj(A) = \frac{|A|}{λ}$ , |A|=6

By putting λ= 1 ,2, 3 Eigen values of adj(A) are 6, 3, 2.