Question: Consider the matrix pipn A: rImrI puw: i (a) Write down A A13 and Find the characteristic polynomial |A AIgl of A, where A is

Consider the matrix pipn A: rImrI puw: i (a) Write down A A13 and Find the characteristic polynomial |A AIgl of A, where A is a variable. 0 (b) Consider the following equation |A A13| = 0 Which are all solutions to the above equation ? 0A1=1,/\\2=1and)\\3=3 'A1=0,A2=land)\\3=3 0A1=0,A2=1andx\\3=5 (c) Let A1, A2 and A3 be the solutions of the equation in (b). We know that A1, A2 and A3 are all eigenvalues of A. Please find eigenspaces Exp Em and 3x3- (d) Find three non-zero vectors 171, 172 and 173 so that for z' = 1, 2, 3, we have that A12; = Agni. (e) Consider the following matrix where 171, 172 and 173 are defined in (d). Please write down the matrix P and nd the inverse P'1 of P (f) Compute P'lAP

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