Question

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 A= = 66 -2) a) The characteristic polynomial is p(r) = det(A – r1) = b) List all the eigenvalues of A separated by semicolons. 1;-2 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue.

Answer 1

Colly A=/ 16 (a) (A-111-11-1 o 21 1²4 1-2 (1+2) (1-1) => x= -2, I (b) - 2,1 let 11 -2 12 = 1 (c) d) considy IA-XII = 0 2-6); (2) (3) (7) > (3) - x - 282=0 = x4=2x2 6. -3 R1 BL 1. l coneidu (A-d₂ I) = OT 22=0 оо (6) => X = (34) =(4) Col4 *22