Question

[2 1 37 A = 0 3 2 To o 2 a) Find the eigenvalues of A. b) Find algebraic multiplicity of each eigenvalues of A. Bonus Find geometric multiplicity of each eigenvalues of A.

Answer 1

solution a 1 Giney! Matix , A = [2 137 To 32 0 0 2 elgen values of A = 2 a) 60, 1A-AI | 30 Ja-nl I 3 Hos7c =0 100 2-0 718-0) [(3-4) (24) -o ].-14(0) +32(0) -0 of (2-1) (3-d) (and) ao 7 1 = 2,2,3 l egen rakes of A)

b) algebric multiplicity of each elgen values of A 7 3) algebote auctiplicity. It is the Амья » Ему ми и Valuu is repeated as a root of the Скала село чоманъч. — o for a=d, algebie muulliplicity o for ad arger obic_мицiplity - 1:3 1 1. — c) geometrie multiplicity. The Girl of ои и у Ра и долни от -10 был равя $1. — бум в д-А 2 Reduce the matrix as A-8I .

UAIL = А- ХТ 2-3 т 2 Т. | 09-22 o o 2-- doing Готэ o 2 Lo o o Rit Re-R2 operation i we get — го о 11 HTo 12 Lo o o — Ra Ra - dR1 А-ЯТ. І. again New), у. Гү, 7 — — и, (А- хт) - 0 -LV, — From above. V = V₂ = 0 гю, taxta viz steace, aulане /

DATE 2. Menet, spay for dedes ? him for did I 1. Aus) ) for A = 3; A-31212-3 1 3 2 Lo s-3 g too 2.8 1-1 1 3 T Loo 2 7 R2/2 L00h 5- 1 3 1 6 7 8 Ph To Tz LOON 100ī -Loo-1 Th Rp 83TR2

DATE Го тя 7 Lр оо N, Го гэдгу, ) гоо | | LO Oo yo tv, tv, = 0 — Y20 K , V =0, а = 0 и ў Г1 440 vity Сима, грам — 1:3 11 ru, Grm of deg i I. Aus)