3. Properties of Affine Sets. Suppose C c R" is an affine set.(a) Consider K points x1,..., Xg € C. Show thatmm2 0;X; € C,for >0; = 1,0; e Ri=1i=1(b) Consider the set S = {x – y, x, y e C}. Show S is a subspace.

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O Consider K points x1,..., X € C. Show that 0;x; € C, for >0; = 1,0; e R i=1 i=1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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Question

3. Properties of Affine Sets. Suppose C c R" is an affine set.
(a) Consider K points x1,..., Xg € C. Show that
m
m
2 0;X; € C,
for >0; = 1,0; e R
i=1
i=1
(b) Consider the set S = {x – y, x, y e C}. Show S is a subspace.

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