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Suppose T: R2 R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from the domain. With this limited information about T, what properties of T can be determined? y y 8 7 6 เก 5 4 3 2 1 8 7 6 5 v2 4 3 * 一个 2 ल x -1 -2 ཌ མ ག -4 -5 -6 -1 -2 -6 TT 44 -3 -4 T(v2) -5 -7 -7 -8 -8 -8-7-6-5-4-3 -2 -1 1 2 3 4 5 6 7 8 -8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 domain codomain ▸ Part 1: Finding eigenvalues using geometry Part 2: Properties eigenvectors Answer the following questions about the properties of the linear transformation T. a. If possible, find another eigenvector for T parallel to V1 but not equal to V1. If it is not possible, enter DNE. b. Is every nonzero vector parallel to V1 an eigenvector for T with eigenvalue 2? choose c. How many nonzero vectors are eigenvectors for T with eigenvalue 2? choose d. Is every eigenvector for T with eigenvalue 2 a nonzero vector parallel to V1 ? choose e. What does it mean geometrically for the eigenvector V₁ to have eigenvalue 2? It means that for any vector v parallel to V1, the linear transformation T choose

Suppose T: R2 R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from the domain. With this limited information about T, what properties of T can be determined? y y 8 7 6 เก 5 4 3 2 1 8 7 6 5 v2 4 3 * 一个 2 ल x -1 -2 ཌ མ ག -4 -5 -6 -1 -2 -6 TT 44 -3 -4 T(v2) -5 -7 -7 -8 -8 -8-7-6-5-4-3 -2 -1 1 2 3 4 5 6 7 8 -8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 domain codomain ▸ Part 1: Finding eigenvalues using geometry Part 2: Properties eigenvectors Answer the following questions about the properties of the linear transformation T. a. If possible, find another eigenvector for T parallel to V1 but not equal to V1. If it is not possible, enter DNE. b. Is every nonzero vector parallel to V1 an eigenvector for T with eigenvalue 2? choose c. How many nonzero vectors are eigenvectors for T with eigenvalue 2? choose d. Is every eigenvector for T with eigenvalue 2 a nonzero vector parallel to V1 ? choose e. What does it mean geometrically for the eigenvector V₁ to have eigenvalue 2? It means that for any vector v parallel to V1, the linear transformation T choose

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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Suppose T: R2 R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from the domain. With this limited information about T, what properties of T can be determined? y y 8 7 6 เก 5 4 3 2 1 8 7 6 5 v2 4 3 * 一个 2 ल x -1 -2 ཌ མ ག -4 -5 -6 -1 -2 -6 TT 44 -3 -4 T(v2) -5 -7 -7 -8 -8 -8-7-6-5-4-3 -2 -1 1 2 3 4 5 6 7 8 -8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 domain codomain ▸ Part 1: Finding eigenvalues using geometry Part 2: Properties eigenvectors Answer the following questions about the properties of the linear transformation T. a. If possible, find another eigenvector for T parallel to V1 but not equal to V1. If it is not possible, enter DNE. b. Is every nonzero vector parallel to V1 an eigenvector for T with eigenvalue 2? choose c. How many nonzero vectors are eigenvectors for T with eigenvalue 2? choose d. Is every eigenvector for T with eigenvalue 2 a nonzero vector parallel to V1 ? choose e. What does it mean geometrically for the eigenvector V₁ to have eigenvalue 2? It means that for any vector v parallel to V1, the linear transformation T choose
Transcribed Image Text:Suppose T: R2 R2 is a linear transformation. The figure shows where I maps vectors V₁ and V2 from the domain. With this limited information about T, what properties of T can be determined? y y 8 7 6 เก 5 4 3 2 1 8 7 6 5 v2 4 3 * 一个 2 ल x -1 -2 ཌ མ ག -4 -5 -6 -1 -2 -6 TT 44 -3 -4 T(v2) -5 -7 -7 -8 -8 -8-7-6-5-4-3 -2 -1 1 2 3 4 5 6 7 8 -8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 domain codomain ▸ Part 1: Finding eigenvalues using geometry Part 2: Properties eigenvectors Answer the following questions about the properties of the linear transformation T. a. If possible, find another eigenvector for T parallel to V1 but not equal to V1. If it is not possible, enter DNE. b. Is every nonzero vector parallel to V1 an eigenvector for T with eigenvalue 2? choose c. How many nonzero vectors are eigenvectors for T with eigenvalue 2? choose d. Is every eigenvector for T with eigenvalue 2 a nonzero vector parallel to V1 ? choose e. What does it mean geometrically for the eigenvector V₁ to have eigenvalue 2? It means that for any vector v parallel to V1, the linear transformation T choose
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