Question

12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/4 0 -1; 01/26; 1/204) (20 pts)Find the inverse of the matrix from question 12. I

Answer 1

1 2 2 C -- AI a NL O - -- O 2 D 2 C ch.pdynomial (-1)(6-4).(-2) -0+ • ( ) + (044) (1-1)/2-3-4**#*)+1(14) - (-:) ( 2-7A+ ht cheq (+-+) (22.2m78 +5) () ( 2x² pod to $(7) = 2d ²-9 dt 5 De di,da = + 9 + 181-4.2.5 2.2

Nina2 = 9 3 581-40 9 2 Jul mots of act T h Eigen vectors ht A-d I = a 6 - R3-7R, an + E - o=?ngtin- Ingle rt и 0 Com an eigen Neelor of Top

Now न 4 CA-I = 1 Instb D ५ ५. १५/पा -1-चा ५ 24 2 -7-4 . 13 7- -1 4 -- Ins-t- D 2 -1-पा 7) Q 0 6 R₂ + (7-541 ) R3 -1-14 + b E O प En C

1 x + tuzo Gu2 (-7- J41) x + 24320 puz = (t + Jul) x dz (7+ Ju trur M the eigen vector wort. d = a + Jut 9- Jui Now, take AdI - 7+ [41 ME 니 4 7+191 6 Rp 7 R R3 R₂ + Ri

"नपा -दा ५ D C R 17 24 ++वा ५ 0 O -1 41 O ० 6 -1 दान + (1 न 43 AGM2-0 । M0 24 - (+-पा) 2 MY । M2 1-पा corr, to पि। eigenvector म.उदा

eigen vectors 17+JUT Inverse: A= 1 2 0 0 -5 6 tal = + ot 2 1+ T 8 adjA= (1.4-o) -(4.0-4.0) (0642 |-(0.0-6.1) (4.4+++ (1+1) (0.0-1) (0.4-1°) (1.1.000 T -- adj A T 2 3 rt wrt 2. w who wa Anh