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The Gauss-Jordan Elimination Algorithm

DefinitionsThe AlgorithmSolutions of Linear SystemsAnswering Existence and Uniqueness questionsThe Gauss-Jordan Elimination AlgorithmSolving Systems of Real Linear EquationsA. HavensDepartment of MathematicsUniversity of Massachusetts, AmherstJanuary 24, 2018A. HavensThe Gauss-Jordan Elimination AlgorithmDefinitionsThe AlgorithmSolutions of Linear SystemsAnswering Existence and Uniqueness questionsOutline1 DefinitionsEchelon FormsRow OperationsPivots2 The AlgorithmDescriptionThe Algorithm in practice3 Solutions of Linear SystemsInterpreting RREF of an Augmented MatrixThe 2-variable case: complete solution4 Answering Existence and Uniqueness questionsThe Big QuestionsThree dimensional systemsA.

Though our initial goal is to reduce augmented matrices of the form fl A b Š arising from a general real linear system, the algorithms we describe work for any matrix A with a nonzero entry. A. Havens The Gauss-Jordan Elimination Algorithm

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