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.jpgAll required answer provided in above steps.

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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Let A = Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the iaginary "unit"): O p(A) = X² + 21 +1=A1 = -1, and A2 = -1, O p(A) = X² – 1=\1 = -1, and A2 = 1 O p(A) = X² – A +1=A1 = 1, and dz O p(A) = X² + 2A + 2 = A1 = -1+ i, and X2 = -1 - i O p(A) = X – 2A + 2 A1 = 1 + i, and A, = 1 – i O p(A) = X2 +1=\1 = i, and A2 = -i 1 W 000 000 F4 F3 E5
(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?
Please help with parts a,b,c with solution and steps!
snip
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
[4 -1 6] Given that 2 is an eigenvalue for A = |2 [2 1 Find a basis of its -1 8 Eigen space.
Please help with parts d,e,f with solution and steps!
2: Let 10 -1 -1 A = 0. 10 10 -1 -1 10 (a) Find the characteristic polynomial of A. (b) Find the dimension of the eigenspace corresponding to the largest eigenvalue.
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)

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