Here we give basic constructions with vectors and discuss the laws of vector arithmetic. Affine combinations of vectors are particularly important.This is the second lecture of a first course on linear algebra, given by N J Wildberger at UNSW. This course will present a more geometric and application oriented approach to linear algebra.We also look at applications to several problems in geometry, such as the facts that the diagonals of a parallelogram bisect each other, and the medians of a triangle meet at a point.CONTENT SUMMARY: pg 1: @00:08 how to approach the course; geometry with vectorspg 2: @03:08 constructions; translate a vector; create equally spaced points; add two vectorspg? 3: @07:20 constructions; bisect a segment; trisect a segment; subtract vectors pg 4: @12:21 Vector Arithmeticpg 5: 17:43 Affine Combinations;pg 6: 22:43 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: 26:53 The zero vector; Linear independence;pg 8: 29:04 Theorem: The diagonals of a parallelogram bisect each other; proof;pg 9: 34:18 Theorem: The medians of a triangle are concurrent, meeting at a point G which divides each in the proportion 2:1 ; proofpg 10: 39:21 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: 41:22 exercise 2.2; exercise 2.3 (THANKS to EmptySpaceEnterprise)
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