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' =
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' =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9348d578-66ea-4064-b97e-301aeae52239%2Fe69bd8b4-b15b-4ab7-a3c7-a4ac86b31273%2Foobgly_processed.jpeg&w=3840&q=75)
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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