Question

I need help with two of these problems

Find a matrix P that diagonalizes A = [ 2], then determine P-1AP. Find A” where A = [~ -5 2 and n is a positive integer. -3

Answer 1

o A 5 2 2 z the roots of 0 eigenvalues 1 A- & Il-o 1112]-[A JA 7 | (s) 2 1 = 2 -1). (5-X) (2-2) -4 = 0 1-67 (0-1) o x = 6 eigenve for corresponding to d=6 (A-6 I) (a) = 0 1 2 2 - 4 21 0 & (7) y eigenrector converponcily to d = 1 A-I) (x) o

2 4 2 classmate Date Page %= (8) ti) u p 2 - 2 - A PDP-1 where D = [6o @ A 4 -3 find An. 2 4 - 5 -30 31 -18 19 A² 31 -18 - 30 19 (214 215 - 129 128) 4-5 - 3 2 like wise of me can follow the potten the the time of matrix Ah n 51-1)" 5x)" 31-12 +5x7h 8 31-1)-3X=;) - SEU = 3x7" 8 8 8