Question

please solve both

7. [-14 Points] DETAILS LARLINALG8 7.1.019. Find the characteristic equation and the eigenvalues and corresponding eigenvectors) of the matrix. - (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (11, 12) = -(C) the corresponding eigenvectors X1 = X2 = Need Help? Read It Watch It Talk to a Tutor 8. [0/5 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.1.021. -1 Find the characteristic equation and the eigenvalues and corresponding eigenvectors) of the matrix. 2 -2 9 0 3 -2 0 (a) the characteristic equation (2-2)(2 - 4) (-1) X (b) the eigenvalues (Enter your answers from smallest to largest.) (14, 12, 13) - ((1,2,4) X the corresponding eigenvectors X1 = (1, -2,9) x X2 = (0,2,-2) x X = (0.-1.1) x Need Help? Read It Watch It Talk to a Tutor

Answer 1

제 Let A : 1 -) 끼 characteristic eq eqa i 승 | 4 - | = 0. 1 - 기 늘 0. - 2. 세 دیاکے 20, + 2 U =0 (1)(1-A) + = - (1-1)(1+1)+ - [- ] + = - + + 0 로 4t3 =0 2 2. 내 | 20 - 1 - 셔를 So, characterstic eq² és 로 120 20,

츠 For engen male solve, 2. 0 - ㅗ 9 =4 SO (1,4> - (2) Let X, be esgeuvector of A Correspondeus to da 2. then 0 (44) = AVI- + 0 - - - 3개+3=0 3 지 전 거 클전 put 2 = 1 빼 들

50 :11 - Let 지 Xz be = eugenvector of a comesponding to 1=1 2 then (4-1/2) x2 = 0. 23 늘 JO -3 -3 X2 co rya 2 +H₂O x=-X₂ put X₂=1 then 4,=-1 Go X, - *