More Row Reduction With Parameters - Wild Linear Algebra A

This lecture develops row reduction with parameters for solving systems of linear equations. It applies parametric solutions to lines, planes, plane intersections, and expressing vectors as linear combinations.

Syllabus

CONTENT SUMMARY: pg 1: @ row reduction using example; get all leading entry values to 1; fully reduced row echelon form; glorified highschool algebra done very systematically;
pg 2: @ example 2 2 parallel lines in a plane; no solution; example 3 3 equations, 3 variables; back substitution;
pg 3: @ definition: Fully reduced row echelon form; examples;
pg 4: @ examples; obtaining fully reduced row echelon matrices;
pg 5: @ Parameters; example a line; parametric solution;
pg 6: @ example a plane; parametric form for a plane: point on plane and 2 direction vectors;
pg 7: @ example intersection of 2 planes in 3D;
pg 8: @ why introduction of parameters works;
pg 9: @ 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: @ problem1 continued;
pg 11: @ problem2: writing 2d vector as a linear combination of 3 other 2d vectors;
pg 12: @ problem2 continued;
pg 13: @ exercise 14.1;
pg 14: @ exercise 14.2;
pg 15: @ exercise 14.3; THANKS to EmptySpaceEnterprise