1. Vector Spaces•Prove that the set of all polynomials of degree at most n forms a vector space over R.Determine its dimension.•=Let VR³ and define a subset W={(x, y, z) Є R³ | x + y + z = 0}. Prove that Wis a subspace of V and find its basis.

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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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1. Vector Spaces • Prove that the set of all polynomials of degree at most n forms a vector space over R. Determine its dimension. • = Let VR³ and define a subset W = {(x, y, z) Є R³ | x + y + z = 0}. Prove that W is a subspace of V and find its basis.