Consider the following.(a) Compute the characteristic polynomial of A.det(A – \I) =A₁ =(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)2₂A ==10 0 189 8-1 0 8^3 =has eigenspace span-4)spanhas eigenspace↓ 1has eigenspace span↓ ↑(c) Compute the algebraic and geometric multiplicity of each eigenvalue.has algebraic multiplicityand geometric multiplicityλ₂ has algebraic multiplicityand geometric multiplicity23 has algebraic multiplicityand geometric multiplicity(smallest λ-value)(largest λ-value)

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Answered: onsider the following. a) Compute the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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.
4 Find A" where A = You are given that the eigenvalues of A are 3 and 4 with corresponding eigenvectors -2 3 and 1 [4" 2(4"-3")] 0. 3" 4h 0. (-2)" 3" 0. 2(3-4") 3" || 3n 0. 2(4-3") 4" None of these.
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).
(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.
5 -3 -5 -2 -1 -B-:-| ,V₂ = 0 1 Find the eigenvalues of A, given that A = and its eigenvectors are v₁ = The eigenvalues are and 1 -1 4 2 -1 and V3 = 1 [:] -1
Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. 3 0 A = [ A₁ = 3, x₁ = (1, 0) 2₂ = -3, x₂ = (0, 1) 0 -3 AX1 ~-[D-F= -0) --- 3 = 0 -3 3 *-*«DE÷-0→ AX2 = = = ไป = 22x2 ↓ 1
Consider the following. A₁ = A = (a) Compute the characteristic polynomial of A. det (A-AI)=-23-32² d₂= 5 50 0 -9 1 1 1 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^3 = -1 0 (LF has eigenspace span has eigenspace span has eigenspace span ↓1 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity λ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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
(b) Let C³ - - 1²: B = 1 c² C-3 0 0 с -C² ³+1 " where ce R. How many eigenvalues does B have and with what ge- ometric multiplicities? Without knowing c, is it possible to determine whether B is diagonalizable? Explain your answers.
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.
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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