Question

Find the eigenvalues and associated eigenvectors of the matrix

Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8

Answer 1

A -3 - 9 -2 3 18 for Eigenvalue (A-ATI = 0 7-d 0 -9 -2-1 3 18 (7- [1-2-1) 6-8-7) - o -o - 3 1 0 - 181-2-1)] (7-1) [ 16+21 +84 +1?] 3[-06-2-1)] 1!2 + 341 + 564 +712- 164 242 – 812-13 - 108 - SAN 3 - 3x² + 4 3 +3 1²4 3 + 4x² +42-42- 4-1² x(x² + 42+4) – 1 (x² + 4x + 4) = 0 (-1) +41+4) =0 (A-1) (+2)2 = 0 Hence: eigenvalue 1 - 2

Now Fineling egenvector corresponding to erginvali A-1 = 7-1 0 1-2 3 18 O -3 9 -3 3 18 o R3 R3-3R, and R2 R2 + 3 R 6 - 3 O No w C R, Ri 6 R2 -R2 3 G thome 2 0 The system associated with cebone matrix - 166

2,-**3 = 1/2 x3 x2 + x3 =0 -> 13--123 6 we take xz = t X2 = 2 Therefore, 7 - lit t = ! ze A - 2 A À I 12 -2+2 w 18 - 072 g O - 3 9 0 3. 0

R2 R₂ + R, and R₂ R₂ - 2R, 9 - 3 1 0 0 O R, Ri 9 Home 3 O O O The system associated uite above mahrie. ܗܚܞ O 0 0 0 2 - 3 X320 2; = 23 we face 1 %22S Then 1 - wit H2=5 z = t Therefore : V- t

dit s=1 t-o 0 r2 = let sao t = 1 !) سار) Hence; Eigenvalue ܟܡܚܪ Eigenvector - 1/2 Eigenvalue - 2 ; Eigenveltor 1 ♡

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