Answered: Given a matrix A with eigenvalues…

Given a matrix A with eigenvalues λ1,···,λn, Calculate the values of the following (show the procedure): (a) det(A3 + A−5 + 3I) (b) tr(( 1/3 A−1 + 5I)−1)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 29CM

See similar textbooks

Similar questions

FIND the eigenvalues of the following matrix: [−3 −1] B= [ 2 −5]
Q3: Find the eigenvalues of the matrix c = (?3 2
x1 = x2 – 4x + 4x3 %3D 4 x½ = -3x2 - V3x, + V3x1 +X3 x3 = 7x2 - 2x1 Find the eigenvalues and eigenvectors by using the above equations.
Solve for p(λ) = det(A−λI).
For a matrix M, Mv Av, evaluate = (Mv)*v in two different ways to find a condition on the eigenvalues 2.
(a) Find the eigenvalues and eigenvectors of the matrix A. Call them A1 and A2 and the corresponding eigenvectors v(1) and v(2). (b) Show that l2 = 1; and v2) = v(1)*, where the * indicates complex conjugation. %3D
The 3 x 3 matrix A has eigenvalues a, 2 and 2a. Find the values of a, 6 and 0 for which 4A-¹ = A²+A+BI3 and A¹ = 0A² + 2A — 4Ī3. a = 1, B = 4, 0=5 a = 1, B = -2, 0=5 a = -1, B2, 0 = 5 a = -1, B = -2, 0=5 a = -1, B = -2, 0=-5
A 2x2 upper triangular matrix A has eigenvalues a and - 5 (with a ≠ -5). An eigenvector corresponding to the eigenvalue a is (1,0). Which of the following could be the matrix A? A. (-5 a/2 0) B. (a 0/2 -5) C. (-5 2/0 a) D. (a -5/0 2) E. (a 2/0 -5)
For #1(c), use diagonal factorization please.
For the matrix, list the real eigenvalues, repeated according to their multiplicities. The real eigenvalues are (Use a comma to separate answers as needed.) 6 0 0 0 3 0 3 646 047 003
Given the eigenvalues: λ = -5 and -2, find an invertible matrix P and a diagonal matrix Q for the following: -11 3 -9 -5 0 O 6 -3 4 PLEASE ENTER YOUR ANSWERS IN THE ORDER λ = = -2, -5 Use two decimal places where required. Matrix P Matrix Q
For the 2 × 2 matrix A, indicate which of the following vectors are eigenvectors, and for those that are eigenvectors, give the corresponding eigenvalue.