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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. HavensThe Gauss-Jordan Elimination AlgorithmDefinitionsThe AlgorithmSolutions of Linear SystemsAnswering existence and uniqueness questionsEchelon FormsRow Echelon FormDefinitionA matrixAis said to be inrow echelon formif the followingconditions hold1all of the rows containing nonzero entries sit above any rowswhose entries are all zero,2the first nonzero entry of any row, called theleading entryofthat row

De nitions The Algorithm Solutions of Linear Systems Answering Existence and Uniqueness questions Echelon Forms Row Echelon Form De nition A matrix A is said to be in row echelon form if the following conditions hold 1 all of the rows containing nonzero entries sit above any rows whose entries are all zero,

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