5.2 please only write on paper. no explanation needed. Questions: 1, 5, 7, 13, 14, 17 on paper Everything is provided don't block for no reason

Exercise Set 5.2 In Exercises 1-4, show that A and B are not similar matrices. 10. Follow the directions in Exercise 9 for the matrix 1. A = 3 2 B = 3 - 2 3 0 0 2 0 2. A = 2 . B = 2 4 2 In Exercises 11-14, find the geometric and algebraic multiplicity of each eigenvalue of the matrix A, and determine whether A is diag- m N HOO 1 B = onalizable. If A is diagonalizable, then find a matrix P that diago- 0 1 0 nalizes A, and find P-1AP. H T -9 -61 4. A= 11. A = - 3 4 Him = 12. A = 25 -11 - 9 HN H - 3 17 - 9 -4 10 0 0 5 0 0] In Exercises 5-8, find a matrix P that diagonalizes A, and check your 13. A = 0 0 0 14. A = 1 5 0 work by computing P-1AP 0 1 10 1 5 In each part of Exercises 15-16, the characteristic equation of a 5. A= 6. A = -14 12 matrix A is given. Find the size of the matrix and the possible dimen- sions of its eigenspaces. 15. a. (1 - 1) (1+ 3) (1 -5) =0 7. A = 0 OHH HOO omo Nom b. 12 ( 2 - 1 ) (1 - 2) 3 = 0 9. Let 16. a. 13(12 - 51 - 6) = 0 A = | b. 13 - 312 + 31- 1=0 In Exercises 17-18, use the method of Example 6 to compute th a. Find the eigenvalues of A. matrix All b. For each eigenvalue 1, find the rank of the matrix MI - A. 17. A = 2 _ 18. A = _1 2 c. Is A diagonalizable? Justify your conclusion