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Consider the linear transformation T: RR whose matrix A relative to the standard basis is giver A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁, 2₂) = 5,6 (b) Find a basis for each of the corresponding eigenspaces. { -2,1 { 1,1 (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors fou B₁ B₂ = = A' = 5 0 0 6

Consider the linear transformation T: RR whose matrix A relative to the standard basis is giver A = (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁, 2₂) = 5,6 (b) Find a basis for each of the corresponding eigenspaces. { -2,1 { 1,1 (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors fou B₁ B₂ = = A' = 5 0 0 6

Advanced Engineering Mathematics
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: RR whose matrix A relative to the standard basis is given. 4 A = 4- [2-7] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁. 12) = 5,6 ],) (b) Find a basis for each of the corresponding eigenspaces. B₁ = {-2,1 B₂ = (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors foun A'= 5 1.1 0 Need Help? E Read It 0 6 Watch It I - 11 1.C 48. S
Transcribed Image Text:Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. 4 A = 4- [2-7] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁. 12) = 5,6 ],) (b) Find a basis for each of the corresponding eigenspaces. B₁ = {-2,1 B₂ = (c) Find the matrix A' for T relative to the basis B', where B' is made up of the basis vectors foun A'= 5 1.1 0 Need Help? E Read It 0 6 Watch It I - 11 1.C 48. S
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