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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The charactertistic polynomial of the matrix C = is p(x) = x²(x - 1). The matrix has two distinct eigenvalues, >₁
6) kindly correctly and handwritten
{-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?
5. Consider the matrix (a) Compute the characteristic polynomial of this matrix. (b) Find the eigenvalues of the matrix. (c) Find a nonzero eigenvector associated to each eigenvalue from part (b).
34) just tell me the correct one and polynomial
(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.

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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.