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CONTENT SUMMARY: pg 1: @ how to approach the course; geometry with vectors

pg 2: @ constructions; translate a vector; create equally spaced points; add two vectors

pg 3: @ constructions; bisect a segment; trisect a segment; subtract vectors

pg 4: @ Vector Arithmetic

pg 5: Affine Combinations;

pg 6: general affine combination of vectors a and b; a way of describing the line parametrically; coefficients of the vectors add up to 1;

pg 7: The zero vector; Linear independence;

pg 8: Theorem: The diagonals of a parallelogram bisect each other; proof;

pg 9: Theorem: The medians of a triangle are concurrent, meeting at a point G which divides each in the proportion 2:1 ; proof

pg 10: Theorem concerning the ratio of 2 parallel vectors a and b contained by 2 vectors c and d radiating from the same point; exercise 2.1 Varignon's theorem

pg 11: exercise 2.2; exercise 2.3 THANKS to EmptySpaceEnterprise

Introduction

Constructions

Vector Arithmetic

Affine combinations

A special vector

Diagonals of a parallelogram

Description:

Explore fundamental concepts of vector geometry in this 44-minute lecture from the "Wild Linear Algebra" course by N J Wildberger at UNSW. Learn basic vector constructions, arithmetic operations, and affine combinations. Discover how to translate, add, subtract, and bisect vectors. Examine important theorems about parallelograms and triangle medians. Apply vector concepts to solve geometric problems, including proofs for the bisection of parallelogram diagonals and the concurrency of triangle medians. Gain insights into linear independence and parametric line descriptions using affine combinations. Practice with exercises on Varignon's theorem and other vector applications to enhance understanding of this geometric approach to linear algebra.

Geometry with Vectors - Wild Linear Algebra A 2 - NJ Wildberger

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#Mathematics #Algebra #Linear Algebra #Geometry #Vectors