Let V be an n-dimensional vector space. We call a subspace of dimension n-1 a hyperplane. a) If : VF is a nonzero linear functional, prove that ker() is a hyperplane b) functional. Prove moreover that every hyperplane is the kernal of a nonzero linear (c) More generally, prove that a subspace of dimension d is the intersection of n-d hyperplanes (ie, from part b, is the intersection of n-d kernals of linear functionals).

Let V be an n-dimensional vector space. We call a subspace of dimension n-1 a hyperplane. a) If : VF is a nonzero linear functional, prove that ker() is a hyperplane b) functional. Prove moreover that every hyperplane is the kernal of a nonzero linear (c) More generally, prove that a subspace of dimension d is the intersection of n-d hyperplanes (ie, from part b, is the intersection of n-d kernals of linear functionals).

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 43EQ

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