Question

(1 point) Let -9 -1 10 A = -4 2 -7 -1 If possible, find an invertible matrix P so that D = P-AP is a diagonal matrix. If it is not possible, enter the identity matrix for Pand the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P = D = Is A diagonalizable over R? diagonalizable Be sure you can explain why or why not.

Answer 1

Eigon values of A det (A-dI)=O gisen by -9-1 ale Io -1 .4 4 2-A 8-A 7 (-9-A) ((2-A) (8-A)-4) +1 (4 (8-A)-28) +10 (-4+7 (2-d)) - (-9-A) (16-21-8A+ 4) (32-41-28) + lo (-4 14- 7) Qニ C-9-4) (-10 + 12)- 4d+ 4 )-70 100 -A+1od-12-9+901-l08-41+4-70 A+100 = 0 0ニ 2 -2 4d-4=O + C-1) C-2=0 Eigen Values 2, 1 ale l Now Jot Did sigen Vectols

A -9%-4+10z = - 2% 4loz= 7X 4x+2y- 4z= -2y 4x- 4z=- 49 %= -+z hena -4+l0z= -7 +7Z 6y--3P here the eigon Vecto d-2 is -1 2 A 2 Z -92-y +10Z= 2% -4+ 10N= l1 X 4x+2y- 4z=2y and -y= Z = X hence the eigen Vetor 2 is

A ZJ -9%-Y+10 z = X y+1oz = 10x 4 x +2y-4z=y 4x-4z=- hence 4x-4z+ loZ = lo x and Cigen Vactos f= us 2 P = - I D = 2 -1 2 Constauctod biuth Costoreponding eigon Value Cenitucted iith eigen Vectos eliagonali Sable Dateuminant of A is nen-Zeas A js Singulas malbia.thaditon to that A diagenalise Se A s on- has 3 distint eigen Values, e we Can A. r A