Question

Linear Algebra. Please do problem 4 parts a-e. I need all steps clear and concise. I will rate you

4. Find all eigenvalues of the following matrices and find one eigenvector associated with each eigenvalue.

Answer 1

A=['i Zhapetostic Poly nomal 1A-17) - 1-) o 01-1 = x -21+1=0 12-1-) H=0 =) +C+1)-1(2-1)=0 .-) 1=1 / Eigeon vecty Asscrialed a=1 1 A-111 188][*]=[:] = 0; X; FOX, where x, and X Both asti tory CH R= [] -)-10 thosectors to polynomial LA-VI) = & +21+1=0 > Ezttl=0 =) (++) (4+1)=6 = =+,-) Eigeon vecty Associated 1=- 1 A +1] - 100][*]-[:] where x, and I arbitry.

Eigears) & A = [os] characterstic Polynomial 1A-11) = 3-4 ] 0-3-1 - 3+1-6=0 » ?+31-21-6=0 =) *[++3) -2(173)=0 - +3) (-2)=0 -) =,-3 Eigen recty when If 1202 TA- 2I) 5. X=0 and a arbitrey So Eigem vecty - 4 If y=-3 5 1 A +31) = ) 5%,+ X2 = 0 *2 = -541 so =) - 8 e spon [5]3 (a) A-107] Choselsfic polynomial IA-II/= :) - |- [r

= 3+1=0 = 5=) =)) -1,7 Eigen recty when it - =) JA-I) - CILD) 1-17:0 G -2X220 = x2 = 0 +) X, CO E[ 7 = span wahrs [:7-CI+)-13**! If ]=-) 6 Q = Px- ext lx = x=0 - 12=0 Eisen vecks {[:]} (C) A= Tharacteostic Polynomial 17-11): 2 1-21-03) Acame) = 0 1741 HI Čor a Eigeon vecter when t=0 A-0Il = CiNiDEC) = x + 1 =0 =) 29 =-11

--- Xa [1] Eigern vecter = span {[-]} If d=3 1 8-21) – (7-201=[:] -2, tl=6 =) 2=X2 Eigen rects span & D