Matrix: please show all your works

(10) Find the eigenvalues and eigenspaces of C = -6 2 -11 3 (11) Let 95 25 24 F = -196 -53 -48 -164 -42 -43 One eigenvalue of F is 5 and the characteristic polynomial is p()) = -13 - 12 + 21X + 45. Without any electronic aid, determine the other eigenvalues. Next, determine the eigenvectors of F. Row reductions may be done with Mathematica (you cannot use any other command than "RowReduce" here!) Finally, if possible, diagonalize F. (If you cannot, explain why.) (12) Let -13 -28 28 A = 4 9 -8 -8 9 The characteristic polynomial is p()) = -13 + 512 -71 + 3 and one eigen- value is A = 3. Without using any electronic aid, find the other eigenvalues. Now determine the eigenspaces. Is A diagonalizable? If so, carry out the details of the diagonalization. (You can use the RowReduce (and no other!) command from Mathematica to help.) Provided that you were able to di- agonalize A, use the diagonalization to compute e24. Also compute A4