Question

Question 2 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-AP=D. [ 13 0 5 0 -12 0 0 6 1-30 0 -12 0 | 32 0 10 -3) A = 1 P= To o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o 0 0 0 0 0 0 0 0 0 0 0 0

Answer 1

given 113 o d on 1-12 o . 6. A = 1-30 .-12 Opel L.32 o 1o 3] find elgenvalues of matrin A |--|-o . 1 13rd o s ol .-12 ondo b ro - 30 ... -lado • 39 . 10 .-3-1) 14 + 312-942-181.= 0 Id+2)(1-3) (+3) =0 14.20,-3,-2,3) eltenirector for 12o _ IA-d Il x 20 13. o. 5:07 -12 0 0 6 79 1-30 o 12 o m 32 0 0 - 31 J 11 o o 7 0 0 0 0 || Ma o 0 0 || mz To oo ng Не Н = 74 = 6 7 - CS Scanned with CamScanner

eigenvector for A = -2 LIS 0. 5 0.9 1-12 ao 1306 -10ol 32oofo- Lng - n - osny 200 na o : alz = -15 Mine V = 1057 eigenvector for AaB L -12...-3 6 M -3.0. 0 -150 2 32 o 10 of 1 [ng T oo -0.57m 2 lol yol 0 0 1 / My OOIT To oo ona tot Discanned with CamScanner s

0.5140 ng=0 ng tng co s 10.5 elgen vector for. d = -3 116. o s o Tour |-19 3 0 6 1 ngle 1-30 o- golm 1 3 3 0 [o o]Lºg | Jo 1 0 271 My To To 0 1 0 1 1 70 To o oo na Tol 9,20 Hq + 9 na =0 May EO_ to = -2 To ois 0.5 6] 0 -115 - 0 Toli il CS Scanned with CamScanner

! Diagonal matots Sool 1.0 o 3 oL Lo o 0-3 0.5 0.5 o 11. ö - na - 15 rhinol Iloi il 4 LO 2 4 0 0 16 0 B 0 -2 0 - A = pap . . lo os. os ollo on.co 100-110-900 0 +05 - Ollo 0 3 0 o i od 1] 10 0 0.-31 Olot CT 130 SO A = -12 ooh S7-30 0 -1 38 o to CS Scanned with Candscamher