Find all eigenvalues of the matrix A-XXT. Find all eigenvalues of the matrix A-XXT.
8.2.35. Given an idempotent matrix, so that P = P2, find all its eigenvalues and eigenvectors. 8.2.35. Given an idempotent matrix, so that P = P2, find all its eigenvalues and eigenvectors.
22. Comber the matrix A-5 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (e) Do you think that the set of the eigenwectors of A is as for the sector space Re? (Justify your answer) (5 pts)
Problem 5. (20 points) 1) Find all the eigenvalues of the matrix A SE 1 2 31 2) Find all the eigenvalues of the matrix A = [32]
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A= Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
Find the eigenvalues and associated eigenvectors of the matrix Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it is possible to diagonalized, then diagonalize the matrix. If it is not possible to diagonalize, then explain why? Show all the work. (20 points) 54 -5 A = 1 0 LO 1 1 - 1 -1