Supposé T: R is a linear transformation. The figure shows whereT maps vectors vi and V2 from the domain. With this limited information about T, what properties of T can be determined? 8 7 6 5 3. 3 1 -1 -2 -2 -3 -5 -6 -7 -- -8 -7 -6 -5 -4 -3 -2 -1 2 3 45 67 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 1 domain codomain - Part 1: Finding eigenvalues using geometry If v, and vz are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) • T(v1) = V1 • T(v2) = V2 Part 2: Properties eigenvectors
Supposé T: R is a linear transformation. The figure shows whereT maps vectors vi and V2 from the domain. With this limited information about T, what properties of T can be determined? 8 7 6 5 3. 3 1 -1 -2 -2 -3 -5 -6 -7 -- -8 -7 -6 -5 -4 -3 -2 -1 2 3 45 67 8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 1 domain codomain - Part 1: Finding eigenvalues using geometry If v, and vz are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) • T(v1) = V1 • T(v2) = V2 Part 2: Properties eigenvectors
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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Transcribed Image Text:Suppose T : R² → R² is a linear transformation. The figure shows where T maps vectors v, and v2 from the domain. With this limited information about T, what properties of T can be determined?
8
8
6
5
-4
T(v1)
-1
-1
|-2
|-2
-3
-4
-5
-6
-7
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8
-8 -7 -6 -5 -4 -3 -2 -1
2 3 4 5 6 7 8
1
domain
codomain
• Part 1: Finding eigenvalues using geometry
If vị and v2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers)
• T(v1) =
V1
· T(v2) =
V2
Part 2: Properties eigenvectors
Part 3: Properties of eigenvectors
Part 4: Is every vector an eigenvector?
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