Question

MH2802-LINEAR ALGEBRA FOR SCIENTISTIS Quiz: Quiz 8: Details of Perspective This Question: 1 pt 3 of 11 Let the matrix below act on C2. Find the eigenvalues and a basis for each eigenspace in C 11-27 Find a basis for the eigenspace corresponding to the eigenvalue a-bi, where b>0. Choose the correct answer below. 04.0:1 oc. * 001 Click to select your answer(s).

Answer 1

Given matrix from ce is Ail, az for finding eigendues consider TA-dIl = 0 where I is identity matrix of dimension 2x2 IA-dil=0 ind -2 Ti 3-d L (1-1)(3-2) +2=0. (:1 1 = ad-bo) 3-1-3dt d² +2=0 12.40 +5 -0 .. which is quadratic equation in d. for finding roots of equation compare with axt bx + C =0 har b = - 4, r= 5 da -ot V6240c 29, = -(-4) + √(-412_4x185 - ut J 16-20 ur J-4 2 Tstamined with CS CamScanner

= 4+ Jū i 2 = 4 + 2 i 2. d 2 Ei i _Now iwo eigenvalues are 2+142-1 eigem.vector at d=2+1, *- TAL/I )x= 0 THEN where x = TI-(2+1) I :-? . 3-(2+i T-1-1 -2 x=0 Li 1-i Ria Ricl-i) R2: R2 (-2) -2(1-) TG-inci-i) 1(-2) -2 (1-1) d u its T-iti-i ti? -2(1-) T |--2 (1-21 -2 -1-1 -211-i) -261-i) J 1-2 hea Scanned Lith 2 CamScanner -2 (1-1) -2 (1-1) |

R2: R2-R, -2 Le -2(1-1) The o Lezy IXLEO -- 24-261-i) x2 zo -200 = 211-i) x2 - 24 = (iinxs 245 - (1 - i) xs is ( 1 - puy ) - Re: -(1-i). . The eigenvector is 34 -It! X2 is correct, 1 . option cs Scanned with CamScanner L ast Minh