Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. 3 -1 A = 2 (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22) = 4,5 (b) Find a basis for each of the corresponding eigenspaces. B₁ = -{(1,-1) B2 {(1,2) (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' =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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Consider the linear transformation T: RR whose matrix A relative to the standard basis is given.
3 -1
A =
2
(a) Find the eigenvalues of A. (Enter your answers from smallest to largest.)
(21, 22) = 4,5
(b) Find a basis for each of the corresponding eigenspaces.
B₁ =
{(1,-1)
B2
(1,-2)
=
(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' =
Transcribed Image Text:Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. 3 -1 A = 2 (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22) = 4,5 (b) Find a basis for each of the corresponding eigenspaces. B₁ = {(1,-1) B2 (1,-2) = (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' =
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