5.3 (a) • Start from A,B,C be non-collinear. (why do you have that?) Can you look at line LAB, IBC, ICA (why these give you lines?), and find one more new point D, E, F on each of them? • Now can you find another point on AE, say point G? 5.3(b) • Can you first recall a projective plane of 7 points that you have seen in tutorial? (the Fano plane) • Can you show that every projective plane of 7 points is isomorphic to the Fano plane? (We will discuss more on isomorphism in detail this Thursday, although you probably have already heard of this from the tutorial.) 5.3(c) We have listed many examples when verifying the axioms of incidence during lecture, you might want to review that part, to be honest, many of the examples there still work =) (for sure I vill help you review the independence on Thursday)

5.3 (a) • Start from A,B,C be non-collinear. (why do you have that?) Can you look at line LAB, IBC, ICA (why these give you lines?), and find one more new point D, E, F on each of them? • Now can you find another point on AE, say point G? 5.3(b) • Can you first recall a projective plane of 7 points that you have seen in tutorial? (the Fano plane) • Can you show that every projective plane of 7 points is isomorphic to the Fano plane? (We will discuss more on isomorphism in detail this Thursday, although you probably have already heard of this from the tutorial.) 5.3(c) We have listed many examples when verifying the axioms of incidence during lecture, you might want to review that part, to be honest, many of the examples there still work =) (for sure I vill help you review the independence on Thursday)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 5AEXP

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