MAT 1341 Lecture Notes - Lecture 13: Gaussian Elimination, Linear Independence, Row Echelon Form
17 Nov 2016
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Lecture 13: solving systems of linear equations (gaussian elimination) Sometimes it"s hard to determine linear dependency if the numbers aren"t elementary. Learning the following technique for solving linear equations will bypass this issue. We want to look at solutions to the following equation: homogeneous linear system: when all rhs (right hand sides) are 0. This is a linear system with equations and variables. When we evaluate a linear system, we"re looking to find the set of all solutions that satisfy all the equations above simultaneously. Assign a free parameter solution to the linear system. 11. 2 examples and vocabulary inhomogeneous solution: not all rhss are 0 degenerate equations one solution no solution infinitely many solutions. Homogenous linear systems are always consistent because is always a possible solution. Any linear system with a degenerate inhomogeneous equation is inconsistent. a) b) Any linear system has either 0, 1, or infinitely many solutions.
