Consider the linear transformation T: R → R whose matrix A relative to the standard basis is given. A = [1 -2] 4 (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). 185 ↓ ↑ A' =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the linear transformation T: RR whose matrix A relative to the standard basis is given.
1-2
1 4
A =
(a) Find the eigenvalues of A. (Enter your answers from smallest to largest.)
(2₂₁, 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' =
Transcribed Image Text:Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. 1-2 1 4 A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₂₁, 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' =
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