A. Let V = L(R², R³). Let U = {T € V : T(x, y) = (ax, by, 0) for some a, b ≤ R}.a) Prove that U is a subspace of V.b) Find a basis of U.c) Find a subspace W of V such that V = U☺W.

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Answered: A. Let V = L(R², R³). Let U = {T € V :…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 40EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V= F, W=finF:f(0)=1

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A. Let V = L(R², R³). Let U = {T € V : T(x, y) = (ax, by, 0) for some a, b ≤ R}. a) Prove that U is a subspace of V. b) Find a basis of U. c) Find a subspace W of V such that V = U☺W.