Question

\text { Let } A=\left[\begin{array}{rrr} 2 & 2 & -1 \\ 1 & 3 & -1 \\ -1 & -2 & 2 \end{array}\right] You are given that det(A – AI)

= -(A – 1)²(A – 5). a) Find the eigenvalues of A. b) Find the corresponding eigenspace E, for each eigenvalue A of A. What is the dimension of E,? c) Diagonalize A by finding an invertible matrix P and a diagonal matrix D such that A = PDP-1. (You do not need to compute P-'.)

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5