Suppose T : R² → R2 is a linear transformation. The figure shows where T maps vectors v₁ and V₂ from the domain. With this limited information about T, what properties of T can be determined? y y 8 40 7 6 5 4 3 2 1 8 7 6 5 v2 4 3 2 7(91) 1 Х T -1 -2 3 x -1 -2- -3 -4 T(v2) -5 5 -6 -6 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1)= ■ T(V2) = V2

Suppose T : R² → R2 is a linear transformation. The figure shows where T maps vectors v₁ and V₂ from the domain. With this limited information about T, what properties of T can be determined? y y 8 40 7 6 5 4 3 2 1 8 7 6 5 v2 4 3 2 7(91) 1 Х T -1 -2 3 x -1 -2- -3 -4 T(v2) -5 5 -6 -6 -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 If V1 and V2 are eigenvectors for T, find their corresponding eigenvalues. If not, enter DNE. help (numbers) V1 T(V1)= ■ T(V2) = V2

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...

See similar textbooks