Wild Linear Algebra 2: Geometry with vectors - YouTube


Wild Linear Algebra 2: Geometry with vectors





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Uploaded on Mar 7, 2011

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 vectors
pg 2: @03:08 constructions; translate a vector; create equally spaced points; add two vectors
pg 3: @07:20 constructions; bisect a segment; trisect a segment; subtract vectors
pg 4: @12:21 Vector Arithmetic
pg 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 ; proof
pg 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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Screenshot pdf's for the lectures are available at http://www.wildegg.com/divineproporti...

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/

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