Let A[1](a) Find the characteristic polynomial of Ap(x) =(b) Find the eigenvalues of A and bases for the associated eigenspaces:Smallest eigenvalueBasis for the associated eigenspace: { }Largest eigenvalueBasis for the associated eigenspace: {}

Let A be a square matrix, then The characteristic polynomial is given by p(x)=det(A-xI) , where I…

Answered: Let A - 63 (a) Find the characteristic…

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 = = -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?
Consider the matrix 0 1 0 0 0010 0001 1000 (a) Find the eigenvalues by finding the characteristic polynomial and looking at its roots. (b) Find the eigenvalues by setting up a system of equations Ar = λ and solving the easy system of equations in the variables x1, x2, x3, x4 for possible X's. (c) For (each/the) eigenvalue, find the corresponding eigenvectors and eigenspaces.
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -3 0 ^= (-2) A 9). a) The characteristic polynomial is p(r) = det(A - rI) = (r+3)(r-4) b) List all the eigenvalues of A separated by semicolons. -3;4 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 side by side in a matrix. If there is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue. ab sin (a) ∞ a ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. 08 f C X
Consider the following. (a) Compute the characteristic polynomial of A. det(A - AI) = -2³ +72² +172 +9 A₁ = A = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = 4 05 6-1 6 5 04 23 = has eigenspace span has eigenspace span has eigenspace span ↓ 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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Let A - 63 (a) Find the characteristic polynomial of A p(x) = 0 (b) Find the eigenvalues of A and bases for the associated eigenspaces: Smallest eigenvalue Basis for the associated eigenspace: { } largest eigenvalue