Question

[عدل]

11 0 10 0 1 1 0 Find the eigenvalues and the corresponding eigenvectors of the matrix 0 0 2 0 Lo 0 0 2]

Answer 1

Given Matrix 0 - O 2 0 o Eigen valuver characteristic Equation = |A-AB120 O O O O O 0 (1-d) Cird) (2-d) (2-d) ao 1 d=lor da londozon diz in Eigen Values are d=1 with multiplicity of? d 22 with multiplicity of 2 Eigen Vectors: 0 for del: [A-1] A-2] - 0 O Redwing the matre, We ger 0 0 (4-as) < O O

let be the eigen vector 3* Jr Solving (A-di] (n) = we get in. u y z >>> y=0 2-0 "18) "41] **8 w=x=1 then 11 and 16 are the eigen vectors for del for d=2= [A-22) - - 6 o 0 0 Solve [A-28] [2] 6 wity zo xty to X y

ĪT way X=4 J ::22 [ ] and are the eigen vectors for 1:2 Therefore, given matrix has eigen valur, A1,1,2,2 and the eigen avectors are and -