Group 3.A =00010 35 43021100a) Determine the characteristic polynomial of matrix A.b) Determine justifying the eigenvalues of matrix A.c) For each eigenvalue of A, determine justitying a base for his eigenspace.d) Determine justifying if it is possible to obtain an invertible matrix P thatP-¹AP is a diagonal matrix, and in case it is, indicate a diagonal matrixof A and an invertible P such that A -= P¹AP.

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Answered: A- 0001 0354 3021 1000 a) Determine the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let A be a 2 x 2 matrix such that A? = A. a) Use an example other than identity matrix to show that A = 0 and 1 = 1 are the only possible eigenvalues of A. b) Find matrix P that will diagonalize the matrix that you have created in (a).
2 3 Let A = Find, 4 1 a) Find the eigenvalues and eigenvectors of A. b) Verify that det(A) is the product of its eigenvalues. c) Is matrix A diagonalizable? If yes, find matrix P and diagonal matrix D such that A = PDP-¹, otherwise explain why not. d) If matrix A is diagonalizable, compute A" and write the final result as a 2 × 2 matrix.
Q2) Let 23 - 222 – 32 be the characteristic polynomial of a matrix A. (i) Determine the eigenvalues of A. (ii) Is A invertible? Justify. (iii) What is the rank for 2I - A for each eigenvalue of A. | (ii) Find 4 and trace(A²).
Calculate the characteristic polynomial of the following matrix A, and use it to compute the eigenvalues of A. -8 4 A = 14 4 6 -2 4 -6 How to enter polynomials: something like 2- 3*r + 4*r^2 - 5*rA3. Remember to use * for multiplication! Enter the characteristic polynomial of the matrix A: Note: Use r as the polynomial variable. Enter the eigenvalues of A separating them by commas: something like 1, -2, 5.
Determine the characteristic polynomial and the eigenvalues for the matrix. A =0 -50
Please help, in order to review for a test:
Please explain step by step how to do parts a, b ,c with the solution

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A- 0001 0354 3021 1000 a) Determine the characteristic polynomial of matrix A. b) Determine justifying the eigenvalues of matrix A. c) For each eigenvalue of A, determine justitying a base for his eigenspace.