Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. 2 A- [4²] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) -([ (21, 2₂) = (b) Find a basis for each of the corresponding eigenspaces. B₁ = 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' =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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Consider the linear transformation T: R → Rn whose matrix A relative to the standard basis is given.
2
A-[4]
=
7
(a) Find the eigenvalues of A. (Enter your answers from smallest to largest.)
-([
(2₁, 2₂) =
(b) Find a basis for each of the corresponding eigenspaces.
{[
B₁
B2
=
A' =
=
(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).
1
Transcribed Image Text:Consider the linear transformation T: R → Rn whose matrix A relative to the standard basis is given. 2 A-[4] = 7 (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) -([ (2₁, 2₂) = (b) Find a basis for each of the corresponding eigenspaces. {[ B₁ B2 = A' = = (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). 1
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