Problem 3 Suppose the vectors u, v, w are linearly independent. Show that the vectors u + v, u - v, u - 2v + w are also linearly independent. Problem 2 Show the following, • Let V = C(1,∞) the vector space of continuous functions on the interval (1,∞). Is the set {log(x³ — x² - x + 1), log(x + 1), log(x − 1)} linearly independant? • Is the set {ex, e²x} is linearly independent ● Find a subset of {cos²(x), 1, cos(2x), sin²(x)} that is linearly independent and is maximal(i.e. adding any additional vector makes the subset linearly dependant)

Problem 3 Suppose the vectors u, v, w are linearly independent. Show that the vectors u + v, u - v, u - 2v + w are also linearly independent. Problem 2 Show the following, • Let V = C(1,∞) the vector space of continuous functions on the interval (1,∞). Is the set {log(x³ — x² - x + 1), log(x + 1), log(x − 1)} linearly independant? • Is the set {ex, e²x} is linearly independent ● Find a subset of {cos²(x), 1, cos(2x), sin²(x)} that is linearly independent and is maximal(i.e. adding any additional vector makes the subset linearly dependant)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 10EQ

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