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3) (9 points) For each of the following matrices Find the eigenvalues and associated eigenvectors. If...
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 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
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
Publish using a MatLab function for the following: If a matrix A has dimension n×n and has n linearly independent eigenvectors, it is diagonalizable.This means there exists a matrix P such that P^(−1)AP=D, where D is a diagonal matrix whose diagonal entries are made up of the eigenvalues of A. P is constructed by taking the eigenvectors of A and using them as the columns of P. Your task is to write a program (function) that does the following If...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
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/
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
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
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 A= = 66 -2) a) The characteristic polynomial is p(r) = det(A – r1) = b) List all the eigenvalues of A separated by semicolons. 1;-2 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them...
4(b) please 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. 1 -2 3 1 2 (a (b) 2 6 6 2 1 13 3 -3 -5 -3 5. Diagonalize the matrix A = if possible. That is, find an invertible matrix P and 2 1 Inc.