Question

C Math Resultat X Reute x Clel 1-X CION X Solutions x Seluler x Seluler x Solutir: x Solution X 3 coeux Full Au X + C app.crcaiak.com/tudent/assets/math-2203-77-linal-exam-2020 Q7 (12 points) th Let 2 0-1 My Courses A- 1 1 -1 Linear Algebra II (MATH-2203-7... 0 0 1 Applied Math for Business and ... (a) Find the eigenvalues of A. (b) Find the corresponding eigenvectors to each eigenvalue of A. (c) Find the corresponding eigenspace to each eigenvalue of A. Moreover, find a basis for each of the corresponding eigenspace. (d) Determine whether A is diagonalizable. If it is, find a diagonal matrix D and an invertible matrix P such that P AP = D. + Drag and drop your files or click to browse... Time left Show © Help Type here to search 1 9 е 2 л re ENG 1:48 PM 2020-37-30

Answer 1

Q. 7. 2 A= Let & be an eigen value of A Now, det (A-2 I 3x3 - 1 2-X => 1. -1 1-) 1-X = (1-1){ ca-a) (1-1) - oyed 7 (1-1)(2-2) - 2=1, 1, 2 ligen values of of A are 11,2 be the legen Vector of A let a2 X3 Corresponding to ligen vake 34 2 az a2 -) x3 23

34 224 - X₂ x4+x2 - 13 2x Az 24 x - 3 4+ 22 - 3 n2 24 23 let KEIR x₂ =K. =k. also let n₂ = C, GEIR :. 4 = 23 K 24 X3 K K, CER legen vector Corresponding to 1 (:). 6) Let be eigen Vector Corresponding to = 2 Similarly we get, 24 - Az 24 4+ 22-dz 202 " az ao :. 34-22

14 egon dectorales 24 6 ) X, ER eigen vector Corresponding G to x=2 rs o © ligen space of x=1 ewм, Asa a 3x k te :K, CER .com - a Span ) : Basis of Et is linearly independent Borisoty). (:(:), :) ligen space of x= 2 XEM 3x1 : Aa=2a = 12 * (6) : MERY

s span Basis for E2 Geometric multiplicity of a=1 algebraic multiplicity of x=1 & Geometric multiplicity of a 2 = 1 algebraic multiplicity of a=2 : A is diagonalizable. - 1 1 Let p = 6 1 - det P -1&o Ta 11 17 p' exists 11661-1o tool - 12.1 l. H1011 -10 1 +1601 + t 1 + 1 = -1 1 - +1 -- 11 +1 +1 1 0 + G

(0) () (0) o 1 О 0 0 2