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Math 2331 Linear Algebra - 1.7 Linear Independence

Linear IndependenceMath 2331 Linear Linear IndependenceJiwen HeDepartment of Mathematics, University of jiwenhe/math2331 Jiwen He, University of HoustonMath 2331, Linear Algebra1 / Linear IndependenceDefinition Matrix Columns Special Linear IndependenceLinear Independence and Homogeneous SystemLinear Independence : DefinitionLinear Independence of Matrix ColumnsSpecial CasesA Set of One VectorA Set of Two VectorsA Set Containing the0 VectorA Set Containing Too Many VectorsCharacterization of Linearly Dependent SetsTheorem: Linear Dependence and Linear CombinationJiwen He, University of HoustonMath 2331, Linear Algebra2 / Linear IndependenceDefinition Matrix Columns Special CasesLinear Independence and Homogeneous SystemExampleA homogeneous system such as 1 2 33 595 93 x1x2x3 = 0

1.7 Linear Independence De nitionMatrix ColumnsSpecial Cases Special Cases: 1. A Set of One Vector Sometimes we can determine linear independence of a set with minimal e ort. Example (1. A Set of One Vector) Consider the set containing one nonzero vector: fv 1g The only solution to x 1v 1 = 0 is x 1 = : So fv 1gis linearly independent when v 1 ...

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