Question

WHMWK 12 Due Thursday by 1pm Allowed Attempts 1 Points 10 Submitting a file upload Fi Available Jul 29 at 12am - Jul 30 at 11:59pm 2 day Q1) Let A = 2 0 1 3 2 2 0 -1 0 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue. Q2) Let ai, 22, 23, 24, as be real numbers. Compute det (GO) ()(O))) Q3) Determine all values of x ER such that matrix 4 0 1 3 5 2 2 A= is invertable. . 0 0 0 0 1 4 0

Answer 1

AS I 3.1 2 2 0 The characteristic equation of A in 2-7 3.02 al 2 0-2 (2-2)823-10-2) +243 ») (2-0) 2-3a tore24 20 (2-2) (ar-3022) 20 (2.2) Cara) (2-1) 20 a = 2, 2, 1 @ eigen values of a are 2, 2, 1 a = 1 or is an eigen value of algelinic mutiplicity 1 and 2 is an eigen value of algebric multiplicity 2 A = a.x Ч 20 6 n 1 3 - 1 2 2 6 13 ny V ):( :) 2 m 14 n, e3n2-23 am tem 201=nis nao me3n2-nz - 2 nit 202-13=6 2x2-13 = 0 inte azon s n2 = 2 my N3 m3 1/2 1 M nz n3

e eigen vector corresponding to eigen Nalue vectoa is A = 1 () 2014 eigen space - Hence geometric multiplicity of the digen value lis 1 for a = 2 A XZ XX sny na302-23 2n & anz 201 202 Pa 2n 2 m na 302 - 2202 2) x, in nat Us an, t2n2=203 > ni niena ength3 m2 ne n2 n3 n3 i eigen vectors corresponding to eigen a= 2 bare value 3 till! ligen space . Hence geometric multiplicity of the eigen value 2 2 [since eigen space contains 2 vectors

② basis of eigen space corresponding to eigen value value lin basis of eigen space corresponding to eigen 2 in Beyy valve algebric multiplicity and geometic multiplicity of eigen walue I in 1 and 1 respectively. algebric multiplicity and geometric multiplicity of eigen value 2 is 2 respectively, 2 and 9.2) - dle det (198)193) 10:14:31:)) des (9.), det (9-) ), det (925) det (946).der (95) .10-1). (0-1). (0-1).(0-1). (ori) (-1)5 = -1 I can not am en tremly sorry. solve (0.3). Please forgive me.