2 In each of the following cases, determine whether the subset W is a subspace of the given vector space V. Justify your answers: check the two closure axioms, the zero axiom and the negative axiom, and say which if any fail. (a) V = R², W = {(x, y) : x, y ≤ R, x>0}. (b) V = R³, W = {(x, y, z) : x, y, z € R, z = x + 2y}. (c) V = M₂ (R), W = {2×2 matrices with integer entries}.

2 In each of the following cases, determine whether the subset W is a subspace of the given vector space V. Justify your answers: check the two closure axioms, the zero axiom and the negative axiom, and say which if any fail. (a) V = R², W = {(x, y) : x, y ≤ R, x>0}. (b) V = R³, W = {(x, y, z) : x, y, z € R, z = x + 2y}. (c) V = M₂ (R), W = {2×2 matrices with integer entries}.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 5RQ

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