Let V=R^2, let H be the subset of V of all points on the line y=3x, and let K be the subset of V of all points on the line y=2x. Is H U K nonempty? is H U K closed under addition? Is H U K closed under scalar multiplication?

Let V=R^2, let H be the subset of V of all points on the line y=3x, and let K be the subset of V of all points on the line y=2x. Is H U K nonempty? is H U K closed under addition? Is H U K closed under scalar multiplication?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 51EQ

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Question

Let V=R^2, let H be the subset of V of all points on the line y=3x, and let K be the subset of V of all points on the line y=2x.

Is H U K nonempty?

is H U K closed under addition?

Is H U K closed under scalar multiplication?

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