Transcription of The Gauss-Jordan Elimination Algorithm
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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.
4 5 6 12 3 7 5 from last time. 1 The entry a 11 = 1, so we can pivot down, using the row operations R 2 R 1 7!R 2 and R 3 4R 1 7!R 3. This transforms the matrix into the row equivalent matrix B 1 = 2 6 4 1 1 1 6 0 3 2 0 0 9 2 12 3 7 5: A. Havens The Gauss-Jordan Elimination Algorithm
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