Question

DETAILS LARLINALG8 7.R.004. Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. --8 1 2 011 005 (a) the characteristic equation of A A= (b) the eigenvalues of A (Enter your answers from smallest to largest.) (2, 22, 2₃) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 1 = basis for the eigenspace of 12 basis for the eigenspace of 13 =

Answer 1

8 L2 1 S Characteristic equatim = (A-AI -8-) il 2 in co O → (8-4) (1-1) (5-1) = 0 7 (4+8) (-2) (A-5) 20 a) the characteristic polynomial is (148) (A-1) (A5) = the eigen values of a. are (A, 2, 3) = (-8, 4, 5) b )

:) 2 M ry ( so the eigenveeton (3) for the corresponding o eigenvaw - L. and. 125 (A-51) ) - LO 24 L > My co 0 -4 :) M - 134 +ng +242 = 0 - 412 + x3 =0 qa from 2 rz = 442 from o - 1321 – 22-243 - - X2-802 -132y =-9x2 m= 2 2

21 1 2 3 4 ) 32 UL 4x2 - 2 4 to so the eigenvector Corresporting the legennalee se te is 9/13 1 9. finally A = -8 corresponding eigen vector 1 12- & corresponding igennector 3-5 comesponding ergenrector པ་ (Am)
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