Let S be a nonempty subset of a linear space, and let m dim S dim aff S Consider the set 1 Show that dim cone dim S 1 2 For every x conv S, there exists m 1 points x1, x2, ,xm 1 S such that x conv x1 x2 xm 1 X xeS cone S conv ...

1 2 The affine hull of S is parallel to the affine hull o ...

Let S be a nonempty subset of a linear space, and let m = dim S =dim

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Let S be a nonempty subset of a linear space, and let m = dim S =dim aff S. Consider the set

1. Show that dim cone = dim S + 1.
2. For every x ˆˆ conv S, there exists m +1 points x1, x2,...,xm+1 ˆˆ S such that
x ˆˆ conv {x1; x2; . . . ; xm+1}

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Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

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Question Posted: May 02, 2016 11:29 AM

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Let S be a nonempty subset of a linear space, and let m = dim S =dim

Question:

X \.xeS cone S conv &

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1 2 The affine hull of S is parallel to the affine hull o...View the full answer

Foundations of Mathematical Economics

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