Question

Matrix is given A= (1 ous e R**3 (2 3 1 Questions: A-) Calculate all eigen na bes dod associə led B- Justify that A is diagonalisable and give and one diagonal matrix boso that A= SDS eigenspaces of A. a regular matrix s

Answer 1

A - Page/ 2 Owe PHH1771TTTTTTTT characteristic eqh is 13- 5,1?+ 5211A= 0 S, = brave of A = 6 S2 = Minors of a,, + minore of an + minors of a33 = (6-0) +(2-2) +(3-0) = 6 +0 +3 = 9 Sg - IA) = \(6-0)-0( 4+25 -1 (0+6) 13_68 +91 40 20 1 9999999 :: 609-62 +9) = 0 969-3)?=0 DO v 2-0, 1 = 3,3 are eigen values. egen rector 1) Por do consider [A-27] x=0 - [A-01]x20 si 0 -1 1727 2 3 || | 60 CO L-2 0 2 ZJ o : 2-2-0 B=3]

Page 2"Վno =) 4 91 41 10 Զ + 83 +z 2011։ – 8 Հ 8 = -1 let zat a ge=t, yzat • eigen vector for a zo is a •Գ Մ ՄՄՄՄՄՄՄՄՄՄՄՄՄՄԱՒ ԼՂ for so | 9 Բ 1 2 3 consider [A-8I] x = 0 - 2 0 -))re 1 օ օ օ L- 0 0 -4J 1- | -2.2 = 3 4 | 2 1 =- * - let se=t, za- et է le 3: 8 ::::::::::: «3» «4» - :: .. :) [2] L- 2 )

s Pages ore eigen veetors for 2-3 en Now, A.M. of 2=0 = G. M of 6 -0) = | & A.M of (A = 3) = G.M of (2=3) = 2 :: A is diagonalizable. § 8 = matrie whose columns are eigen veetor. FEC-22222222 [ 1-2 ól Consider,

consider SDS-111 0110 007 TR01 ] _Pagey -1 0 1 0 3 0 1 11-20Jlo 031 | 2 3 ? 1-2 3 o 1 2 I SDS" =