Let S = {3x² − 2x, −2x² + x +4, −3x + 1} ≤ P₂. (a) Show that S is linearly independent. (b) Recall that P2 is a 3-dimensional vector space. Use Theorem 2.10 to conclude that S is a basis for P₂. (c) Express 8x² – 3x + 7 as a linear combination of the vectors in S. What is [8x² − 3x +7]s? - (d) Find another basis for P₂ containing the linearly independent set {8x² − 3x +7}.

Let S = {3x² − 2x, −2x² + x +4, −3x + 1} ≤ P₂. (a) Show that S is linearly independent. (b) Recall that P2 is a 3-dimensional vector space. Use Theorem 2.10 to conclude that S is a basis for P₂. (c) Express 8x² – 3x + 7 as a linear combination of the vectors in S. What is [8x² − 3x +7]s? - (d) Find another basis for P₂ containing the linearly independent set {8x² − 3x +7}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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