Please show step A diagonalization of the matrix A is given in the form PAP D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)| - ܕܐ143114. 142312NAN43 3 3 7 1000111-13326 0-1has elgenspace spanhas eigenspace span-has eigenspace span60 000 00 0 -1(smallest 2-value)48-(largest λ-value)

Given system is P^(-1)AP =D We have to tell eigenvalue and eigenvector . Since we know that the…

Answered: A diagonalization of the matrix A is…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 66E: Show that A=[0110] has no real eigenvalues.

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A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) d₁ = ^₂ = ^3 = 5 6 0 1 6 1 H6OL6 1 6 6 1 0 6 1 1 5 1 1 0 1 0 501 1 0-1 0-1 0 1 1 5 has eigenspace span has eigenspace span 600 0 1 0 ]-[88] = 000 has eigenspace span ↓ 1 → (smallest λ-value) (largest λ-value)
Suppose A is a 3 x 3 matrix whose only eigenvalues are A = -1,0, 3, and suppose B is a 4 x 4 matrix whose only eigenvalues are = -2, 2, 4. For each of the following statements, answer %3D • TRUE if the statement must be true, • FALSE if the statement must be false, or • NOT ENQUGH INFO if there is not enough given information to determine if the statement is true or false. i. A is invertible. ii. B is invertible. A is diagonalizable. B is diagonalizable. iii. iv. V. there exists a nonzero vector v in R4 such that Bv = v. %3D vi. there exists a nonzero vector w in R' such that ||Aw|| = ||w||.
For each matrix below, you are given one of the eigenvalues. Find a corresponding eigenvector for each eigenvalue: 3 1) A = 7 -2 -1 12 -7 and λ = 5. A corresponding eigenvector would be: 12 12 -10_ -8 + 8i 2) B= -12+9i 3) C = -3 + 15i 1+14i -48 +36i -12 +60i -40-25i -95-67i 53 +45i 204 +82i 37 + 15i 88 +45i -49-33i -180-50i 3-6i 3-6i and λ = 4-i. A corresponding eigenvector would be: 16-25i -129-9i 47+21i -317-61i 190 + 49i 616 - 32i 110 + 66i -63-45i -232-75i and λ = 1 + 2i. A corresponding eigenvector would be:

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