1. Is it possible to find three linearly independent eigenvectors for A? 0 0 0 (1)...
2. Find eigenvalues and eigenvectors of the matrix and check if they are linearly independent A - 12 11 Ō SETY (30 marks)
Find a set of linearly independent eigenvectors for the given matrices. Use the power method to locate the dominant eigenvalue and a corresponding eigenvector for the given matrices. Stop after five iterations. 13. 0 1 0 0 0 10 00 0 1 14 6 4 「10 001 121 11 15。 112 21 1112 1. 23 . 「3 00 7. 12 26 6 4 2 35
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12 -8 0 0 | 12 -7 -1 a) Eigenvalues: 4,4, -1; Number of independent eigenvectors: 2 b) Eigenvalues: 4,2, -1; Number of independent eigenvectors: 3 c) Eigenvalues: 4,-2,1; Number of independent eigenvectors: 3 d) Eigenvalues: 4,-2, -1; Number of independent eigenvectors: 3 e) Eigenvalues: 4,-2, -2; Number of independent eigenvectors: 2 f) None of the above.
1) a)Find the rank of A. b) Are the following vectors linearly independent? ſo 1 27 [2] [1] [0] A = 2 0 5 u = 5 uz = 0 uz = 2 0 0 0 To o o 2) What are the eigenvalues and the spectral radius of (4 0 27 B= 0 2 0 Bonus: Find one of the eigenvectors of B. 001
Find two linearly independent set of eigenvectors for the matrix and then solve 1 2 2. -2 6
Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the eigenvalues of A. (b)(2 marks) Explain without any more calculations that A is diagonalisable. ((7 marks) Find three linearly independent eigenvectors of the matrix A. (d)(2 marks) Write an invertible matrix P such that -100 P-AP=0 40 0 0 3
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3 Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3
2 2 2 Without calculation, find one eigenvalue and two linearly independent eigenvectors of A= Justify your answer. 2 2 2 2 2 2 One eigenvalue of A is 0 because the columns of A are linearly dependent. 1 because the entries of each vector are equal. Two linearly independent eigenvectors of A are -1 2 (Use a comma separate answers as needed.)
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
Without calculation, find one eigenvalue and two linearly independent eigenvectors of A2 2 2 Justify your answer One eigenvalue of A is0 because the columns of A are linearly dependent. Two linearly independent eigenvectors of A arebecause (Use a comma to separate answers as needed.) Without calculation, find one eigenvalue and two linearly independent eigenvectors of A2 2 2 Justify your answer One eigenvalue of A is0 because the columns of A are linearly dependent. Two linearly independent eigenvectors of...