Let U, V and W be vector spaces. Let S : U → V and T : V → W be lineartransformations. Define R: U -> W by letting R(u) T(S(u)) for all u Є U.(1) Show that R is a linear transformation.=(2) Show that if S and T are one-to-one, then R is one-to-one.

a) Problem 1: Show that R is a linear transformation.To prove that R is a linear transformation, we…

Answered: Let U, V and W be vector spaces. Let S…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...

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Let U, V and W be vector spaces. Let S : U → V and T : V → W be linear transformations. Define R: U -> W by letting R(u) T(S(u)) for all u Є U. (1) Show that R is a linear transformation. = (2) Show that if S and T are one-to-one, then R is one-to-one.