"线性代数"的相关文档

标签“线性代数”的相关文档，共223条

(1.23)--4.2.5初等矩阵（上）线性代数与空间解析几何典型题解析
初等矩阵与初等变换的关系初等矩阵线性代数与空间解析几何典型题解析矩阵的重要分解初等矩阵及其性质初等矩阵3,12,AABB设为阶方阵将的第列和第例列交换得到再把1的23,.CAQCQ第列加到第列上得到求满足的可逆阵312,AB交换阶方阵的第列和第列得到解答即010100.001BA1000110203,1CBBC将的第列加到第列上得到即010100100011.001001A..;初等矩阵与初等变换...
2024-06-0801.02 MB0
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(1.22)--4.2.4逆阵（下）线性代数与空间解析几何典型题解析
方阵的伴随阵方阵的逆阵求方阵的逆阵的方法逆阵线性代数与空间解析几何典型题解析证明方阵可逆的方法逆阵1(1)(2),(2).AEB求求矩阵2232110121AE(1)写出矩阵解答413110,2.123AABAB设矩阵且例1210,2.AEAE由于||所以可逆1[(2)]EAE[2]AEE初等行变换11||1,AabdbAAAcdcaadbc若则110010043120011011...
2024-06-0801.11 MB0
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(1.21)--4.2.3逆阵（上）线性代数与空间解析几何典型题解析
方阵的伴随阵方阵的逆阵求方阵的逆阵的方法逆阵线性代数与空间解析几何典型题解析证明方阵可逆的方法逆阵1(1)(2),(2).AEB求求矩阵2232110121AE(1)写出矩阵解答413110,2.123AABAB设矩阵且例1210,2.AEAE由于||所以可逆1[(2)]EAE[2]AEE初等行变换11||1,AabdbAAAcdcaadbc若则110010043120011011...
2024-06-0801.14 MB0
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(1.20)--4.2.2矩阵运算（下）线性代数与空间解析几何典型题解析
矩阵运算线性代数与空间解析几何典型题解析矩阵的加减法数乘矩阵矩阵的乘法矩阵的转置方阵的幂1()2XAB2AXB解答由解得矩阵运算的典型题解析30151001,,416121322.ABAXBX设矩阵求使得成立的矩阵例112022.3330221401460332101733322411031121020AB解答41103,11,.21020A...
2024-06-0801.04 MB0
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(1.19)--4.2.1矩阵运算（上）线性代数与空间解析几何典型题解析
矩阵运算线性代数与空间解析几何典型题解析矩阵的加减法数乘矩阵矩阵的乘法矩阵的转置方阵的幂1()2XAB2AXB解答由解得矩阵运算的典型题解析30151001,,416121322.ABAXBX设矩阵求使得成立的矩阵例112022.3330221401460332101733322411031121020AB解答41103,11,.21020A...
2024-06-0801.04 MB0
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(1.13)--3.2.2矩阵的秩（下）线性代数与空间解析几何典型题解析
线性方程组线性代数与空间解析几何典型题解析矩阵的秩定义：矩阵的秩定义：矩阵的秩知识点回顾——矩阵的秩若矩阵A中存在r阶非零子式,而任何r1阶子式(若存在)均等于零,则称矩阵A的秩为r，记为rank()Ar或r()Ar.规定：零矩阵的秩为零.矩阵的秩就是矩阵中最高阶非零子式的阶数.矩阵的秩就是矩阵中最高阶非零子式的阶数.评注：评注：与秩相关的结论与秩相关的结论与秩相关的结论与秩相关的结论(3)初等变换不改变矩阵的秩.(3)...
2024-06-0802.34 MB0
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(1.12)--3.2.1矩阵的秩（上）线性代数与空间解析几何典型题解析
线性方程组线性代数与空间解析几何典型题解析矩阵的秩定义：矩阵的秩定义：矩阵的秩知识点回顾——矩阵的秩若矩阵A中存在r阶非零子式,而任何r1阶子式(若存在)均等于零,则称矩阵A的秩为r，记为rank()Ar或r()Ar.规定：零矩阵的秩为零.矩阵的秩就是矩阵中最高阶非零子式的阶数.矩阵的秩就是矩阵中最高阶非零子式的阶数.评注：评注：与秩相关的结论与秩相关的结论与秩相关的结论与秩相关的结论(3)初等变换不改变矩阵的秩.(3)...
2024-06-0802.34 MB0
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(1.6)--1.2.6克拉默法则线性代数与空间解析几何典型题解析
n元线性方程组的克拉默法则克拉默法则线性代数与空间解析几何典型题解析齐次线性方程组的非零解的判别克拉默法则例1解线性方程组12341242341234258369.2254760xxxxxxxxxxxxxx解答：方程组的系数行列式为21511306270,02121476D由克莱姆法则,此方程组有唯一的一组解其中由克莱姆法则,此方程组有唯一的一组解其中12341234,,,.DDDDxxxxDDDD115130681,89502124...
2024-06-0801.15 MB0
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(1.3.16)--2.5.2线性代数线性代数
LinearAlgebra（2credits）2.5.2SomeResultsfortheRankofaMatrixResultsfortherankofmatrices:0()min{,};RAmnmn()();RATRA()();RARB()();RPAQRAmax{(),()}()()();RARBRABRARB()()().RABRARB(1)(2)(3)Ifthen,AB(4)Ifisinvertible,,PQ(5)(6)AEXAMPLELetbeanmatrix.Provethatnn()().RAERAEn()()2,AEAEEProofSince)2.RAERAERAEREAREn（）（-（）（）（）thenQuestion(...
2024-06-080149.95 KB0
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(1.3.15)--2.5.1线性代数线性代数
LinearAlgebra（2credits）2.5.1RankofaMatrix1.RankofamatrixDefinition1Foranmatrixweselectanyrowsandcolumnsofthenformadeterminantoforderfromtheentriesatthecrossoftheselectedrowsandcolumns,withtheir-ordersunchanged.Thedeterminantobtainedaboveisreferredtoastheoperationsonamatrixarereferredtoasank-orderminorofA.kA,mnk(,),Akmknk2k(,)ijkkmnCCForanmatrix,therearek-orderminors.mnDefinition2For...
2024-06-080213.1 KB0
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(1.3.14)--2.4.3线性代数线性代数
LinearAlgebra（2credits）2.4.3CalculateInverseMatrixbyUsingElementaryOperationsTheinversematrixcanbeobtainedbyperformingelementaryoperations.11AAEEAIfisinvertible,wemayconsiderA112lPPPAEEA112lAPPP，Supposewehave2nn1.ANoteWestartwithanmatrixthenperformelementaryrowoperationsonit.WhenistransformedtomatrixistransformedtoA,AEEE,123221,343A...
2024-06-080219.79 KB0
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(1.3.13)--2.4.2线性代数线性代数
LinearAlgebra（2credits）2.4.2ElementaryMatrixDefinitionIfwestartwiththeidentitymatrixandthenperformexactlyoneelementaryrowoperation,theresultingmatrixiscalledanelementarymatrix.QuestionHowmanytypesofelementarymatricesfromelementaryoperations?(1)Interchangingtworows(columns);(2)Multiplyingarow(column)withanonzerok;(3)Addingamultipleofonerow(column)toanother.11011(,)11011Eij...
2024-06-080309.69 KB0
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(1.3.12)--2.4.1线性代数线性代数
LinearAlgebra（2credits）2.4.1ElementaryOperationsonaMatrixDefinition1Thefollowingthreetypeofoperationsonamatrixarereferredtoaselementaryrowoperations:(1)Interchangingtworows(thei-throwandthej-throw,denotedas);ijrr,denotedas);irk(2)Multiplyingarowwithanonzeroconstant(thei-throw,contantkdenotedas).ijrkr(3)Addingamultipleofonerowtoanother(ktimesofthej-throwtothei-throw,Definition2Elementary...
2024-06-080137.86 KB0
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(1.3.11)--2.3.3线性代数线性代数
LinearAlgebra（2credits）2.3.3PartitionMatrixintoRowsorColumns1.PartitionMatrixintoRows11121121222211nnmmmnmaaaaaaaaAaaaa12TTTmwhere12=TiiiiinaaaaisreferredtoasrowvectorofA.2.PartitionMatrixintoColumns11121212221211,nnnmmmnaaaaaaAaaaaaa...
2024-06-080233.6 KB0
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(1.3.10)--2.3.2线性代数线性代数
LinearAlgebra（2credits）2.3.2OperationsofPartitionedMatrices.11111111srsrssrrBABABABABAsrsrsrsrBBBBBAAAAA11111111,(1)AdditionIfareofthesamedimensionandarepartitionedinthesameway:,ABwhereareofthesamedimension.Then,AB1111rssrAAAAA.1111srsrAAAAA...
2024-06-080349.32 KB0
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(1.3.9)--2.3.1线性代数线性代数
LinearAlgebra（2credits）2.3.1PartitionedMatrixPartitionedMatrixInordertosimplifytheoperationofmatriceswithlargedimension,itisusefultothinkofamatrixasbeingcomposedofanumberofsub-matrices.Amatrixcanbepartitionedintosmallermatricesbydrawinghorizontallinesbetweentherowsandverticallinesbetweenthecolumns.Thesmallermatricesareoftenreferredtoasblocks,whilethematrixwhoseentriesareblocksisreferredtoaspa...
2024-06-080109.17 KB0
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(1.3.8)--2.2.3线性代数线性代数
LinearAlgebra（2credits）2.2.3ProofofCramer’sRuleCramer’sRulennnnnnnnnnbaxaxxabaxaxxabaxaxxa22112222212111212111Anlinearsystem11221()(1,2,,)jjjjnnjDxbAbAbAjnDD0.DnnhasuniquesolutionifthecoefficientdeterminantThesolutionis12nbbbb12nxxx,x111212122212,nn...
2024-06-080134.35 KB0
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(1.3.7)--2.2.2线性代数线性代数
LinearAlgebra（2credits）2.2.2Methodsofcalculatingtheinversematrix1.UndeterminedcoefficientMethodSolutionLetbetheinverseof,dcbaBAThendcbaAB01121001100122badbcaEXAMPLE1.IFcalculate0,112AA1.,1,0,02,12badbca.2,1,1,0dcbaThus.21101...
2024-06-080162.7 KB0
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(1.3.6)--2.2.1线性代数线性代数
LinearAlgebra（2credits）2.2.1InverseofaMatrix1.Introduction,111aaaaFormultiplicationofnumbers,if,thenwhereisthereciprocal(orthemultiplicativeinverse)of.0aaa11aEFormultiplicationofmatrices,identitymatrixisanaloguetothenumber.Formatrix,ifthereisamatrixsuchthat,thenisthemultiplicativeinverseof.1A1A11AAAAEAA12.InverseofaMatrixEXAMPLE12,211212,1111...
2024-06-080316.91 KB0
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(1.3.5)--2.1.5线性代数线性代数
LinearAlgebra（2credits）2.1.5TheDeterminantandAdjointofaSquareMatrix1.TheDeterminantofaMatrix23=68,A23=68A.2SomeRules;1ATA;2AAn;3ABABABBA.DefinitionThedeterminantofasquarematrixisthatwhoseentriesare‘s.ThedeterminantofisdenotedbyorAAAAdet().AForexample,ifthen2.TheAdjointofaMatrixDefinitionIfisanmatrix,thenthematrix112111222212nnnnnnAAAAAAAAAA...
2024-06-080174.23 KB0
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