This video looks at applications of row reduction to understanding linear transformations between two and three dimensional space. It also introduces the important notions of a spanning set and a linearly independent set of vectors.This is the16th lecture in this series on Linear Algebra by N J Wildberger.CONTENT SUMMARY: pg 1: @00:08 More applications of row reduction; How row reduction helps us to understand some? interesting aspects of linear transformations; not necessarily working with square matrices; example;pg 2: @04:05 A transformation where the input space and the output space are not necessarily the same; example: what happens to the basis vectors under transformation?;pg 3: @8:56 analyse previous example using row reduction; the equation of the image plane is obtained by row reduction;pg 4: @14:55 example2: a linear transformation from 3d to 2d;pg 5: @16:53 example2 continued; analysed using row reduction; importance of mapping the basis vectors @19:46 ; some vectors are sent to zero in the transformation;pg 6: @23:02 example continued; row reduction;pg 7: @26:41 Spanning sets; examples; a? unique linear combination;pg 8: @30:28 Spanning sets continued; examples; pg 9: @33:35 use of row reduction to determine whether we have a spanning set; pg 10: @39:19 Spanning sets continued; example2; not a spanning set; pg 11: @41:35 spanning sets continued; 2d space; pg 12: @43:32 linearly independent sets of vectors; examples; a linearly dependent set; pg 13: @45:42 linear independence/dependence continued; examples;? a set containing the zero vector;pg 14: @48:05 linear dependence continued; example1; pg 15: @49:42 example1 continued using row reduction; pg 16: @51:14 linear dependence continued; example2; pg 17:? @52:54 example2 continued; pg 18: @54:10 exercise 16.1; pg 19: @54:41 exercises 16.2-3; pg 20 @55:42 exercises 16.4-5; pg 21 @56:09 exercises 16.6-7; (THANKS to EmptySpaceEnterprise)
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