This video explains the second half of row reduction, a basic algorithm in linear algebra used to solve systems of linear equations. Parameters are introduced corresponding to non-leading columns of the augmented matrix of the system.We apply this to the problem of writing one vector as a linear combination of others, both in the two dimensional and three dimensional situations.This is the 14th lecture of this course on Linear Algebra given by Assoc Prof N J Wildberger.CONTENT SUMMARY: pg 1: @00:07 row reduction using example; get all leading entry values to 1; fully reduced row echelon form; glorified highschool algebra done very systematically;pg 2: @04:56 example 2? (2 parallel lines in a plane); no solution; example 3 (3 equations, 3 variables); back substitution;pg 3: @10:20 definition: Fully reduced row echelon form; examples;pg 4: @12:40 examples; obtaining fully reduced row echelon matrices;pg 5: @15:48 Parameters; example (a line); parametric solution;pg 6: @19:28 example (a plane); parametric form for a plane: point on plane and 2 direction vectors;pg 7: @22:39 example (intersection of? 2 planes in 3D);pg 8: @26:33 why introduction of parameters works; pg 9: @30:32 problem1: writing a vector as a linear combination of 3 other vectors; important point: a system can be thought of? in different terms; pg 10: @33:19 problem1 continued; pg 11: @38:25 problem2: writing 2d vector as a linear combination of 3 other 2d vectors; pg 12: @41:06 problem2 continued; pg 13: @44:06 exercise 14.1; pg 14: @45:02 exercise 14.2; pg 15: @46:51 exercise 14.3; (THANKS to EmptySpaceEnterprise)
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