3. Find all eigenvalues and eigenvectors for the following matrices R= [ { 1]
Find the eigenvalues and eigenvectors of the following matrices 1) Find the eigenvalues and eigenvectors of the following matrices. -5 4 -2.2 1.4 2 0 -1 2 1-2 3
Find the eigenvalues and normalized eigenvectors of the following matrices. Show whether the eigenvectors are orthogonal. (60) (23) (1, 1) (i)
Q1) Find the Eigenvalues and the Eigenvectors for the following matrices 16
Please how all work! 1. Find the eigenvalues and corresponding eigenvectors of the following matrices. Also find the matrix X that diagonalizes the given matrix via a similarity transformation. Verify your cal- culated eigenvalues. (4༣). / 100) 1 2 01. [2 -2 3) /26 -2 2༽ 2 21 4]. [42 28) ( 15 -10 -20 =4 12 4 -3) -6 -2/ . 75-3 13) 0 40 , [-7 9 -15) /10 4) [ 0 20L. [3 1 -3/
3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If possible, state the matrices P and D, such that A = PDP-1. (Hint: P is a matrix containing eigenvectors of A on its columns, and D is a diagonal matrix.) If it is not possible to find P and D, just state so. 11-133b a. A = 1 2 2 1-2 -2 -2 2 0 -1 3] b. A = [1 -4 110 0...
Determine the eigenvalues and corresponding eigenvectors of the following matrices Which of the matrices can be diagonalized?
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
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
5. (Strang 6.1.1) Consider the two matrices: = [:] (4+1)= [ 1 (a) Find the eigenvalues and eigenvectors of both A and (A + 1). (b) How are the the eigenvectors of these matrices related? (c) How are the eigenvalues related?
[12 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. -2 3 (a) (b) 2 3 2 6 -6 2 -1 NN 1