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Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. A-[3] A= (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (A₁, A₂) 4,5 (4,5 (b) Find a basis for each of the corresponding eigenspaces. B₁ 1,2 B₂- (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). A'= X 5 1,1 5 1 2 1

Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. A-[3] A= (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (A₁, A₂) 4,5 (4,5 (b) Find a basis for each of the corresponding eigenspaces. B₁ 1,2 B₂- (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). A'= X 5 1,1 5 1 2 1

Elementary Linear Algebra (MindTap Course List)
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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Consider the linear transformation T: R^ →R" whose matrix A relative to the standard basis is given. [³ A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (1₁, 12) = 4,5 B₂ 3-2 (b) Find a basis for each of the corresponding eigenspaces. B₁ = 1,2 128 1,1 = A' = 1 6 (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). X 5 5 1 2 ↓ 1
Transcribed Image Text:Consider the linear transformation T: R^ →R" whose matrix A relative to the standard basis is given. [³ A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (1₁, 12) = 4,5 B₂ 3-2 (b) Find a basis for each of the corresponding eigenspaces. B₁ = 1,2 128 1,1 = A' = 1 6 (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors found in part (b). X 5 5 1 2 ↓ 1
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