Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. Let T: UV be a linear transformation of vector spaces over a field F, and let WCU be a subspace of U. (a) Show that the function T': WV, given by the formula T'(u) = T(u) for every uЄ W, is a linear transformation (this T' is usually denoted by Tw and called the restriction of T to W). (b) Show that Ker(T') = Ker(T) nW.

4. Let T: UV be a linear transformation of vector spaces over a field F, and let WCU be a subspace of U. (a) Show that the function T': WV, given by the formula T'(u) = T(u) for every uЄ W, is a linear transformation (this T' is usually denoted by Tw and called the restriction of T to W). (b) Show that Ker(T') = Ker(T) nW.

Elementary Linear Algebra (MindTap Course List)
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
icon
Related questions
Question
4. Let T: UV be a linear transformation of vector spaces over a field F, and let WCU be a subspace of U. (a) Show that the function T': WV, given by the formula T'(u) = T(u) for every uЄ W, is a linear transformation (this T' is usually denoted by Tw and called the restriction of T to W). (b) Show that Ker(T') = Ker(T) nW.
Transcribed Image Text:4. Let T: UV be a linear transformation of vector spaces over a field F, and let WCU be a subspace of U. (a) Show that the function T': WV, given by the formula T'(u) = T(u) for every uЄ W, is a linear transformation (this T' is usually denoted by Tw and called the restriction of T to W). (b) Show that Ker(T') = Ker(T) nW.
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
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
SEE MORE TEXTBOOKS