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 8 v2 7 7 6 6 5 4 3 2 1 X 5 4 3 2 1 (v1) -1 -2 -3 -4 -5 -6 -7 -8 T(v2) -8-7-6-5 -4 -3 -2 -1 X -1 -2 -3 -4 -5 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain Part 1: Finding eigenvalues using geometry If v₁ and v₂ are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) ▪ T(v₁) = V1 T(V₂) = V2 1 codomain 2 3 4 5 6 7 8

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 8 v2 7 7 6 6 5 4 3 2 1 X 5 4 3 2 1 (v1) -1 -2 -3 -4 -5 -6 -7 -8 T(v2) -8-7-6-5 -4 -3 -2 -1 X -1 -2 -3 -4 -5 -8 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 domain Part 1: Finding eigenvalues using geometry If v₁ and v₂ are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) ▪ T(v₁) = V1 T(V₂) = V2 1 codomain 2 3 4 5 6 7 8

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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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
8
v2
7
7
6
6
5
4
3
2
1
X
5
4
3
2
1
(v1)
-1
-2
-3
-4
-5
-6
-7
-8
T(v2)
-8-7-6-5 -4 -3 -2 -1
X
-1
-2
-3
-4
-5
-8
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
domain
Part 1: Finding eigenvalues using geometry
If v₁ and v₂ are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers)
▪ T(v₁) =
V1
T(V₂) =
V2
1
codomain
2 3 4 5 6 7 8

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