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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 5 Сл 4 3 2 1 22 v2 8 7 6 5 4 3 2 1 x * -8 -1 -2 -3 -4 -5 879 -6 -7 H↑ -1 -3 ཌ ས ཧ -4 T(v2) -5 -6 -7 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1) = ■ T(V2) = V2 x

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 5 Сл 4 3 2 1 22 v2 8 7 6 5 4 3 2 1 x * -8 -1 -2 -3 -4 -5 879 -6 -7 H↑ -1 -3 ཌ ས ཧ -4 T(v2) -5 -6 -7 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1) = ■ T(V2) = V2 x

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 5 Сл 4 3 2 1 22 v2 8 7 6 5 4 3 2 1 x * -8 -1 -2 -3 -4 -5 879 -6 -7 H↑ -1 -3 ཌ ས ཧ -4 T(v2) -5 -6 -7 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1) = ■ T(V2) = V2 x
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 5 Сл 4 3 2 1 22 v2 8 7 6 5 4 3 2 1 x * -8 -1 -2 -3 -4 -5 879 -6 -7 H↑ -1 -3 ཌ ས ཧ -4 T(v2) -5 -6 -7 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1) = ■ T(V2) = V2 x
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