Question

Question 2 5 pts Find the eigenvalues and their corresponding eigenvectors of: 1 2 2 B 2 5 2 2 -2 1 Hint: Use EROs to create two zeros in one row or one column of B - 1. I first. Upload Choose a File

Answer 1

2 2 | 3 = Solutions 2 - 2 eigenvalues - for | 8 -7 = 0 2 2 لم -۱ 2 - المدل = 0 م - 2۔ 2 - 2 = [رب 2- (د ] (+[- (ی) ] - [(2) - (4-1)(م) ] (-) = و از 5 - با 2 + - کرج - 2 - ری - رو ما را داریم - ی) - = ( - )-) + ۲۶ (-) - 2 [21- ،] + 2 [21- ،] =0 سے 0 = ( - ) به مریم - ره) 0=[ + (5) (2) (ی] و جزو ہے - ام - ) (-) = 0= زو+A-2) (ر) 0 (1-) (3)2 = 6 and d2 = 3 and 13=3 - | eigenvales theree are

eigenvectors, di=1 LB-d, I ] [v] zo 2 1-2 -2 2 5-da 2 210)13) -2 I-do 1-1 2 V 2 2 -2 5-1 -2 0 2 2 -2 2 Y -2 L2 By row 11-13 [!!!][*]-[:)] operation Jo the equating are - V, +}=0 U2+ Uz=0 Div = 0 v=t V = -t Uz -t let Sol -t -t t t

put t=1 g EI & eignerctor coresponding diel. for (in d2=3 [B-d, I] [w]=0 2 2 2 5-3 -2 JE)-1) د اما =2 2 2 2 [-2 -2 2 2 W 2 2 -2 -2 by row operations, [ED] Soi the system of equations, W,- W2- W z=0 o. W2to. W z = 0 o. Wz+o. Wzzo W2=k · Wo =e Wiz kte W ckte W = Wz k Ws

N e [:] К. take Kal, bl So, •{(!] • [!] } are eigensch d=3. along #