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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.2: Orthogonal Complements And Orthogonal Projections

Problem 29EQ

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Question

Which of the following is/are subspaces of R³?
V₁ = R²
0
a
1
{[A]
{B}
V₂ =
V3 = Span
O V₁ and V₂
O V₁ and V3
O V₁ only
O V3 only
O V/₂ only
}
: a is a real number.

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Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.
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