(1.1.9)--英1.3.1克莱姆法则及重要结论.ppt

1.3.1CramersRuleandSomeImportantConclusionsLinearAlgebra（2credits）

Supposelinearequations?thenthissystemofequationsiscalledinhomogeneouslinearequations;?thenthesystemofequationsiscalledhomogeneouslinearequations.Conceptsofinhomogeneousandhomogeneouslinearequations

1、CramersRuleIfthecoefficientdeterminantofthelinearequationsisnotequaltozero,thatis

thenthelinearequations(1)haveasolution,andthesolutionisunique.Thesolutioncanbeexpressedas?Whereisthen-orderdeterminantobtainedbyreplacingtheelementsofcolumninthecoefficientdeterminantDwiththeconstanttermsattherightendoftheequations,thatis,

2、ImportanttheoremsTheorem1IfthecoefficientdeterminantofthelinearEquations(1)isnotequaltozero,then(1)musthaveasolution,andthesolutionisunique.?Theorem2Ifthelinearequations(1)havenosolutionorhavetwodifferentsolutions,thenthecoefficientdeterminantmustbezero.

(1)Thenumberofequationsisequaltothenumberofunknowns;(2)Coefficientdeterminantisnotequaltozero.TwoconditionsareneedtosatisfyinordertoUseCramersRule:3、Summary

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