futher mathematics topic 8 martix

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1、Topic8MATRICES矩阵本章概要8.1kickoffwithcas---4月1日8.2matrixrepresentation矩阵的表示---4月1日8.3addition,subtractionandscalaroperations矩阵的加法，减法，数乘---4月5日8.4multiplyingmatrices矩阵的乘法---4月6日8.5multiplicativeinverseandsolvingmatrixequations矩阵的逆和矩阵方程的解法–--4月7日8.6Dominanceandcommunicationmatrices优势矩阵和通讯矩阵—-4月12日

2、8.7applicationofmatricestosimultaneousquations用矩阵解方程组----4月13日8.8transitionmatrices转化矩阵----4月14日8.9review4月15日-16日Dominantmatrices优势矩阵计算器表示方法Wecanusedominancematricestofindwhichvertexinamatrixisthemostdominant.Thiscanhavemanypurposes,forexampledeterminingtheorderofteamsinaroundrobintournament

3、.问题情境1Fivesoccerteamstookpartinaroundrobintournamentwitheachteamplayingeachotherteamonce.Theresultswereasfollows:•BdefeatedCandE•AdefeatedB,C,andD•CdefeatedE•DdefeatedB,C,andE•EdefeatedA.Giventheaboveresults,trytorankthe5teamsinorder.问题2(menu7)Theseresultscanberepresentedina5×5matrix.Complete

4、thefollowingmatrixbyplacinga1intheelementswheretheteamintherowsdefeatedtheopposingteamsinthecolumns.Placea0inallotherelements.3aUsingCAS,definethecompletedmatrixfromquestion2.bUseCAStodeterminethematrixD^2.cUseCAStodeterminethematrixD+D^2.4Sumeachrowofthematrixfoundinquestion3c.5Useyouranswer

5、toquestion4toranktheteamsinorder(theteamwiththehighestsumisthemostdominantteam,andsoon).6Compareyouranswertoquestion5withyouranswertoquestion1.8.2关键单词序号单词中文1matrix矩阵2element元素3rectangularmatrix矩形矩阵4order秩序，次序5rowmatrix行矩阵6columnmatrix列矩阵7squarematrix方矩阵8diagonalmatrix对角矩阵9zeromatrix零矩阵10symme

6、tricalmatrix对称矩阵11triangularmatrix三角形矩阵12lowertriangularmatrix下三角形矩阵13uppertriangularmatrix上三角形矩阵14binarymatrix二元矩阵TypesofmatricesRowmatrix=AmatrixwithonerowColumnmatrix=AmatrixwithonecolumnSquarematrix=Amatrixwithanequalnumberofrowsandcolumnsiscalleddiagonalmatrix=Asquarematrixthathasonlynon

7、-zeroelementsonthemaindiagonal.zeromatrix=Azeromatrixconsistsonlyofelementsthatare0.symmetricalmatrix=A,matrixneedstobeasquarematrix.AtriangularmatrixAtriangularmatrixisatypeofsquarematrix.Atriangularmatrixcanbelabeledalowertriangularmatrixif