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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.

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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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.
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