Question

Due in 1 hour. very confused please clear explanation. thank you!

associated with the eigenvalues. Find the eigenvalues of A and the 10 4L A= 0 1 -2 the eigenvectors as such: 81 = , should be entered as 17, - 3 be

Answer 1

1 0 4 0 1 - 2 L1 0 -2] Characteristic equation A XIal=0 = -1 O 1 0 4 1-1 -2 0 -2- 0 - (x-1){ (1-x) (-2-2) 54} =0 (x-1){ x²+x-6} =0 = (x-1) (1 +3) (X -2) =0 A = 1, A2=-3, 3=2 The eigen values are xi=1 Az =-3 3 =2 Leny ve = (1) be the eigen vector a elgen value *i=1 Them Av = XIV, = (A - d, Is) v = 0

10 0 41 0 0 - 2 The sug tem of ewation - 213 =0 24 + (-3) ₂=0 ) from 0 , 13 =0 mg = 0, me = mz Len na = 1 Then eigen vector, vi = () Let be the eigen vecton corresponding elyen value X2= -3 Then (A-de J3) V2 = 0 14 0 4 1 / =) To 4 - 2 || 44, + 4 4 3 =0 472 - 243=0 + Ya 0

From (2) 1 (22, Y = - Y3 Y₂ = ŽY choose Yo = 1 Then No = 1 / being eingen vector for X3= 2 iny eigen vector Then (A - Ag53) Ug = 0 1-1 o 4 1/₂1 TO -1 -2 Zz li 0-4/13 - 2 + 4 Zz =0 - 2q + (-2)}=0 2 - 4Z =0 = 42 Z = -23 2 = 1 from ③ Take Them V₂ = (-223 23

being eigenvector Take 3=1, Then V₂ = Eigenvalue Eigen vector x = 1 X = 1 Az = 2 = -2 vow A = 21:14,-, 4, -21 1