please do # 5, 21, 41, 81

In Exercises 1-12. a matrix and its characteristic polynomial are given. Find the cigenvalues of each matrix and determine a basis for each eigenspace. (1 -5)(1 - 6) 2. 26 -2- (1 + 4)(1 + 5) 3. -9 4. 14 12 (/ + 2)(1 -5) 5. -(1 + 3)(1 - 2)2In Exercises 13-24. find the eigenvalues of each matrix and determine a basis for each eigenspace. 13. A w 14. - 12 15. -3 -4 2 12 16. E. 3 -12 17. 18. -OO Low 8 -8 NUB OWL 19. 2 20. OWO -5 4 0 4 OWN 21. 2 22. 2\f81. (a) Determine a basis for cach cigenspace of (b) Determine a basis for cach cigenspace of -34. (c) Determine a basis for each cigenspace of 5A. (d) Establish a relationship between the cigenvectors of any square matrix 8 and those of cB for any scalar c * 0. (e) Establish a relationship between the cigenvalues of a square matrix B and those of cB for any scalar c 0