Question

2) Find the eigenvalues and eigenvectors of following matrix: 10 1 0 (101) \o 1 0

Answer 1

liven matrin AZ 9_0X?+(-1-1)3 - 0 =0 a ca - 2) = 0; 2 0. - = 0 . x = IV:

Find the Eigen recfors (A-DI) a no lo7 1 -O | Lo -o ? If d=0 then 0 cos D x2 =0 2, + 25 =0. 21, = -912 F À = V2 then -12 | 0 N2 0 1

0 0 V2 Vol 0, 1 VZ V₂ 1 - 2 0 V2 R₂ 7 V2 V

-V2 :: 0 71 R27 R, tho t r2 ni 10 V2 / 13 1-12 i olla 10.- 1az R₂ - hz + R2 1. oo o g 2 x + 12 = 0 - 4 + 12 = 0 * -622, +124;=0 -V2.7, -13)=0 4,743 20

If n = V2 then > TV2 uz a löin M2 I 01 911 REVO 9 0 1 12 12 10 R₂ R₂ - R, | o 1 121) R RzRyt ooo ce

V21 R₂7 R Toll 29 12 », try = 0. -96 # 1273 = 0 V29, # V2 Az =. V2 (Ar- g) = 0. 2,-43=0 2. = 43

: Eigen value corresopoing Figen vectors. A AV-2V If a=0 ELM. OLD 10 9 | 0 | Til If d = 12 12 V 2 1 0 V2 V21 of – 12 101 1 -12 101 Tove