Question

If possible diagonalize the following matrix. Write the complete diagonal factorization in the form D=P-1 AP where Dis diagonal and Pis a nonsingular matrix. A (1 8 4 5 [1.

Answer 1

Given A O 4 3 then find its eigen values | A-11120 (S)--[:] 1-2 8 1 (-))(59) -32=0 5-7-57+72-32=0 - 6x + x2 - 27 = o 22-61-2750 72-92 +31-27 co 2(1-9) +3 (9-3) 20 (1-2 (2+3)=0 and 1=-3 eigenvalues, Now eigen veeter Corresponding to eigin value 29 and A2-3 8 s-a 1-9 DAS [$][:] 2 [K[:] S] [5] [3] [***] []+[:] -1633-1: [:] [$+[:] 4 4 -8x, +8x2 = 0 4x + x 2 = 0 4x4 + 8x = 0 x = -242 ut 72 = k then 44,- 470 X = 42 net X2 = K =X1 eigen vector is a eigen vecter is k [+]

Now P= ㅗ I 1] ㅗ and prd a 1/3 2/ -1/2 1/3 then Diagonal Da prap 11 [+][] 213 9 6 11 JO - I / 9 -3 = [3:46 o -3 D [:-]