Question

Find the transition matrix P and the diagonal matrix D such that A = P-DP, if [2 1 1] A 1 2 1 1 2

Answer 1

Az 2 The charadesstic car is b&+91-40 C&D) Cha=0 ~ 1=111,4 op eigenvalues Eigenvertas fatal (A-I) X=0 167-69 OxfXNXZ Optix a BAXHX {x-3-- x = X= Ex X2 01-07 ha X, 4 X2 = 0 907 eigemed as far t=1 Eigonvata 827=4 (4-2)X=0 2 -2 I 1-2 X3

=)=28,7X27);=0 x^2X27X3 =0 X772-23 20 0-0 ->) -3Xp+3Y3 =0 @3) -3%,+3850 x=3 ** X ta x = ха ts -63 [i] Xz = is epenwets f3 1= P=[X1 X2 X3] =) pa - then 8 = ² 2/3 % -/ -1/32 / / /31 Cl bt Pls 43-4 A=plop=1 / 3 / 4 1010 ol 101) 3 / 1004