elementary linear algebra with solutions (matthews 1998)

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1、ELEMENTARYLINEARALGEBRAK.R.MATTHEWSDEPARTMENTOFMATHEMATICSUNIVERSITYOFQUEENSLANDSecondOnlineVersion,December1998Commentstotheauthoratkrm@maths.uq.edu.auAllcontentscopyrightc1991KeithR.MatthewsDepartmentofMathematicsUniversityofQueenslandAllrightsreservedContents1LINEAREQUATIONS11.1Introductiontoline

2、arequations.................11.2Solvinglinearequations.....................61.3TheGauss{Jordanalgorithm..................81.4Systematicsolutionoflinearsystems..............91.5Homogeneoussystems......................161.6PROBLEMS...........................172MATRICES232.1Matrixarithmetic............

3、.............232.2Lineartransformations......................272.3Recurrencerelations.......................312.4PROBLEMS...........................332.5Non{singularmatrices......................362.6Leastsquaressolutionofequations...............472.7PROBLEMS...........................493SUBSPACES55

4、3.1Introduction............................553.2SubspacesofFn.........................553.3Lineardependence........................583.4Basisofasubspace........................613.5Rankandnullityofamatrix..................643.6PROBLEMS...........................674DETERMINANTS714.1PROBLEMS..........

5、.................85i5COMPLEXNUMBERS895.1Constructingthecomplexnumbers...............895.2Calculatingwithcomplexnumbers...............915.3GeometricrepresentationofC..................955.4Complexconjugate........................965.5Modulusofacomplexnumber.................995.6Argumentofacomplexnumbe

6、r.................1035.7DeMoivre'stheorem.......................1075.8PROBLEMS...........................1116EIGENVALUESANDEIGENVECTORS1156.1Motivation............................1156.2Denitionsandexamples.....................1186.3PROBLEMS...........................1247Identifyingseconddegreeequat

7、ions1297.1Theeigenvaluemethod......................1297.2Aclassicationalgorithm....................1417.3PROBLEMS...........................1478THREE{DIMENSIONALGEOMETRY1498.1Introduction............