Consider the following.A₁ =A =(a) Compute the characteristic polynomial of A.det (A-AI)=-23-32²d₂=5 50 0-9 11 1(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)^3 =-10(LFhas eigenspace spanhas eigenspace spanhas eigenspace span↓11(c) Compute the algebraic and geometric multiplicity of each eigenvalue.A₁ has algebraic multiplicityand geometric multiplicityλ₂ has algebraic multiplicityand geometric multiplicity13 has algebraic multiplicityand geometric multiplicity(smallest λ-value)(largest λ-value)

Answered: Image /qna-images/answer/eb27bc4d-977a-4aad-9fee-e14c34f44758.jpg

Answered: Consider the following. A = A₁ = 5 50 0…

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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Please help me solve this. I got to all three eigens are equal to zero by doing subtraction of 5(first equation)-(third equation) and 3(first equation)-(second equation) and then solced out for my "a" "b" and "c" values. where did I go wrong here?? only HANDWRITTEN answer needed ( NOT TYPED)
ul T-Mobile 2:44 AM 37% Let A = Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the imaginary "unit"): O p(A) = X2+ 21 +1=Aj = -1, and A2 = -1, O p(A) = X2-1 =-1, and A2 = 1 O p(A) = X² – 24 +1=A, = 1, and A2 = 1 O p(A) = X² +2A + 2 A1 = -1+i, and A2 = -1-i O p(A) = X2 - 2A +2 A1 = 1+i, and A2 = 1-i O p(A) = X2 + 1=A1 = i, and X2 = -i F3 O00 F4 F5 F7
Verify that A is an eigenvalue of A and that x, is a corresponding eigenvector. 4 -2 = -11, x; = (1, 2, –1) 22 = -3, x, = (-2, 1 0) 23 = -3, x; = (3, 0, 1) A = 2 -7 6 2 4 -2 13 Ax- 2 -7 6. 2 -11 2 !! 2 4 -2 2 AX2 -2 -7 !! %3D !! 4 -2 AX3 2 -7 = 13x3 1
(8) Show that the constant term of the characteristic polynomial |21 – A| is ±JA|. Using this fact, consider the case here A = 0 is an eigenvalue of A. What can you conclude about the invertibility of A, and why?
(i) For which values of c, A has the eigenvalues 0, 3, −3? Find the eigenvectors of A.(ii)Check whether A is digonalizable, and find its diagonal.
A = [ 3² -7] ₁ 1. Let A = (a) By finding the eigenvalues and corresponding eigenvectors, give a diagonalization of A. (b) Without computing directly, find A¹ using the diagonalization from part (a).
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)
Let A (a) Determine the eigenvalues X₁ and ₂ of A where X₁
Define a linear operator I on P₂. by (Tp)(x) = xp'(x) + plo) Write a proof showing that find the eigenvalues and. eigenspaces of 7² 2 and say if I is diagonalizable

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