/ 4 100 (12 pts.) Let A=| 0 -1 0). If it is possible to diagonalize A, find P and D such that A = PDP-1. 0 0 4 If it is not possible to diagonalize A, explain why not.
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
1. Orthogonally diagonalize the following matrices, if possible. If it is possi- on of the matrix ble, give the spectral decompositi 0-3 0 2
4 0 -2 Diagonalize C=125 4|ifpossible, or state why it is not diagonalizable. 3. lo 0 5
Please refer to illustration for question.
Diagonalize the matrix A, if possible. That is, find an invertible matrix Pand a diagonal matrix D such that A = PDP-1. A = -11 0 6 3 -5 -3 -91 0 4 12 A = 1 LO 0 0 2 0 0 2 0 0 0 9 A= 9 0 -16 0 0 0 16 9 4 1 0 0
Diagonalize the following matrix, if possible. 4 9 1 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4 0 A. For P- 04 0 OB. For p D= 07 OC. For P- DE [:-) OD. The matrix cannot be diagonalized,
Question 5. (a) Diagonalize the matrix S = [1 0 -11 -1 2-1 and calculate A100. 1-2 0 0 (b) Diagonalize the matrix A and find a matrix B so that B2 = A. (2 007 (c) Show that the matrix H = 3 2 0 is not diagonalizable. How many linearly independent eigen- LO O 3] vectors does H have?
16. Diagonalize the following matrices if possible. (If not possible explain why not) Then compute A2. (Use the diagonal matrix to do the computation if A was diagonalizable) One of the Eigen-values is provided to get you started. A= [-2 3 1-9 10 -1 15 4 -2 10. 2=4
Problem 5 Diagonalize B and compute XA*X-1 to prove this formula for Be, (sections 6.1, 6.2) Bk=15+ 5+-4k has 0 41, Compute also , end sin 0 4
Problem 5 Diagonalize B and compute XA*X-1 to prove this formula for Be, (sections 6.1, 6.2) Bk=15+ 5+-4k has 0 41, Compute also , end sin 0 4
e Diagonalize the matrices and compute A and B10. 「3000 2 2 A=1141| and B=10200 1 0 0 3
e Diagonalize the matrices and compute A and B10. 「3000 2 2 A=1141| and B=10200 1 0 0 3
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 2 2 -4 - 1 5 -4 ; 2 = 3,8 -2 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 3 0 0 For P = D= 0 3 0 0 0 8 (Simplify your answer.) B. 3 00 For P = D = 0 8 0 0 0 8 (Simplify your answer.)...