89.1.Let A-6 -733(a) Doing all the computations by hand, find the characteristic polynomial of A.(b) Doing all the computations by hand, find the eigenvalues of A and their algebraic andgeometric multiplicities.(c) Find an invertible matrix C and a diagonal matrix D such that C-lAC = D.

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Answered: 8. 9. 1. Let A -6 -7 3 -1 (a) Doing all…

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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{-8, 0, -2} Calculate the characteristic polynomial of the following matrix A, and use it to compute eigenvalues of A. -13 2 9 -13 2 9 -5 2 How to enter polynomials. Enter the formula for a polynomial using * to denote multiplication and to denote the exponent. For example, if the answer is the polynomial A Do not forget to use for multiplication! then you should enter 1 2*x + (3/7)*x^2 + 4.5*x^3. Enter the characteristic polynomial of the matrix A: Note: Use X as the polynomial variable. P(x) = 1-2x + 3 7 +4.523 Enter eigenvalues of A separating them by commas: For example, if you obtain that eigenvalues are 1, -2, and 5 then you should enter 1, -2, 5
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.
Suppose that A is a square matrix with characteristic polynomial (2-3)*(2-4)³ (2+1). (a) What are the dimensions of A? (Give n such that the dimensions are n x n.) n= (b) What are the eigenvalues of A? (Enter your answers as a comma-separated list.) λ = (c) Is A invertible? Yes O No (d) What is the largest possible dimension for an eigenspace of A?
(1) (a) Diagonalize the matrices ($) () 2 -1 11 3 15 and 1 3 -1 -4 -1 -2 2 (The eigenvalues of the second matrix are 1 = 1, 5.) (b) Calculate lim A", where A is the first matrix.
4. 225
(i) (; ) 8 4 4 and are eigenvectors of A 7 7 5 a Use the definition of eigenvalues and eigenvectors to find the eigenvalues of A. b Hence write down the characteristic polynomial of A.
Let A = = -8 2 2 2 2 -5 4 4 (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why?
not a graded assignment, please do (i) and (iii) for a and b.
Please explain step by step how to do parts a, b ,c with the solution

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8. 9. 1. Let A -6 -7 3 -1 (a) Doing all the computations by hand, find the characteristic polynomial of A. (b) Doing all the computations by hand, find the eigenvalues of A and their algebraic and geometric multiplicities. (c) Find an invertible matrix C and a diagonal matrix D such that C-'AC = D.