Question

7 3. Diagonalize A = 1 0 0 0 . Use this diagonalization to compute A". 15 -2)

Answer 1

15 consider ATI 0 7 > B 15 - 2x 1,-1,-2. A has 3 distinct mo and Aisa 33 matrix value A honan eigenvalues comesponding each es eigenvales diagenalizable, man eigurator Then R² has a bon's made of eigenrators of a new Ais A has no Alternatively, characteristic polynomial of A is diagonali pable repeated root so diagonalize A Now let us consider (And I ) x = 0 FO O 15 a x = (1,1,5) gasolution s Xi = (1,1,5) is an eigen ve rater of A correy corresponding to al

consider daarl, aus A-2,9 )X = 0 o 7 0 0 0 is a solution ventor 12 am e > eigen corresponding wazo -2, consider (Araz f)x= to 1 + 0 3 0 o x = (1,0, 1) is a solution * 22 (1,0,1) is an ei eignrector of corresponding to Agar2 A Comida pa - 0 det P o 0 0 - 0 The PAPE 0 0 (p'ap)" = (PAP) (PAP) pt Alp (PAP) (1 times) >> AN PD"pr

Al-PD"pt 2 0-5 f G -2 0 -3 +5.2" 2 1 0 5+5. 2 1 10237 2047 - 10245 2048