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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 x

Each linear dependence relation among the columns of A corresponds to a nontrivial solution to Ax = 0. The columns of matrix A are linearly independent if and only if the equation Ax = 0 has only the trivial solution. Jiwen He, University of Houston Math 2331, Linear Algebra 7 / 17

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