The space P, of polynomials of degree up to n has a basis consisting of polynomials that all have the same degree. A proper subset of a linearly independent set can sometimes form a spanning set. f S is a linearly independent set and T' is a spanning set in a vector space V, then SnT is a basis for V. If {u, v, w} is a linearly independent set, then {2u + 5v + 4w, u + 5v, u + 4w} is linearly independent. f {u, v, w} is a linearly independent set, then {u + 5v, v — 4w, w} is linearly independent.

The space P, of polynomials of degree up to n has a basis consisting of polynomials that all have the same degree. A proper subset of a linearly independent set can sometimes form a spanning set. f S is a linearly independent set and T' is a spanning set in a vector space V, then SnT is a basis for V. If {u, v, w} is a linearly independent set, then {2u + 5v + 4w, u + 5v, u + 4w} is linearly independent. f {u, v, w} is a linearly independent set, then {u + 5v, v — 4w, w} is linearly independent.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 26EQ

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