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Are the following statements true or false? 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 I 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. If {u, v, w} is a linearly independent set, then {u + 5v, v — 4w, w} is linearly independent.

Are the following statements true or false? 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 I 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. If {u, v, w} is a linearly independent set, then {u + 5v, v — 4w, w} is linearly independent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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Problem 3. ? ? ? ? ? Are the following statements true or false? The space Pn 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. If 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. If {u, v, w} is a linearly independent set, then {u + 5v, v − 4w, w} is linearly independent.
Transcribed Image Text:Problem 3. ? ? ? ? ? Are the following statements true or false? The space Pn 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. If 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. If {u, v, w} is a linearly independent set, then {u + 5v, v − 4w, w} is linearly independent.
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