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Math 2331 { Linear Algebra - UH

Echelon FormsMath 2331 Linear Row Reduction and Echelon FormsJiwen HeDepartment of Mathematics, University of jiwenhe/math2331 Jiwen He, University of HoustonMath 2331, Linear Algebra1 / Echelon FormsDefinition Reduction Solution Row Reduction and Echelon FormsEchelon Form and Reduced Echelon FormUniqueness of the Reduced Echelon FormPivot and Pivot ColumnRow Reduction AlgorithmReduce to Echelon Form (Forward Phase)then to REF (Backward Phase)Solutions of Linear SystemsBasic Variables and Free VariableParametric Descriptions of Solution SetsFinal Steps in Solving a Consistent Linear SystemBack-SubstitutionGeneral SolutionsExistence and uniqueness TheoremUsing Row Reduction to Solve Linear SystemsConsistency QuestionsJiwen He, University of HoustonMath 2331, Linear Algebra2 / Echelon FormsDefinition Reduction Solution TheoremEch

Existence and Uniqueness Theorem Theorem (Existence and Uniqueness) 1 A linear system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column, i.e., if and only if an echelon form of the augmented matrix has no row of the form 0 …

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