Conversely, if T :V V is a linear operator such that T2 = T, show that V = kerT O imT. [Hint: 3.b, v - T(v) lies in ker T for all v in V.]

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 3EQ: In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB,...
icon
Related questions
Question
3.b,
Conversely, if T :V → V is a linear operator such that T2 = T, show that V = kerT O imT. [Hint:
v – T(v) lies in ker T for all v in V.]
Transcribed Image Text:3.b, Conversely, if T :V → V is a linear operator such that T2 = T, show that V = kerT O imT. [Hint: v – T(v) lies in ker T for all v in V.]
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning