0 -1 4 -1
AsAigMnNm91e2nt1 IsMmatrixnvertible?Explainyouranswer. QUESTION1 M=0B B@2??10 0 ??14??10 ??14??1 0??121C (3marks) AC: QUESTION2 FindtheigenvaluesforthematrixAwherA=B??3IandBis: B=0@ 41 0 15011A HerBisa33matrix(whicmeansAandIarealso33).; (1) (6marks) QUESTION3 bloIcfkKmantrdicHesa(wrehpcosimtvaendshnitrelexmplaitnswHhyanMMdai=lspoK0HsitaKrv0emdarnictes)b:utNisnotpositvedniteMandNa(2re) and N=K K(3) (6Hmealprk:sC)onectpivotsandeignvaluesofMandNtopivotsandeignvaluesofHandK.
(a)Solvethedierntialequationfor QUESTION4 (w2itmhafrrkes-)xedboundaryconditonsu0()=0andu(2??)d=x2u0.=2 (4) (wbi)thAfrlseo-nxdedthbeoudnidearryncceondqiutaotniosnus0??fo=r02xuan=d2un+or1=??0ui1+h2ui??ui??1=2 (5) mWselacarHoitcenhdft:ysroFufdorers-atehccxxoeaunddtarbscortyui.snbudeTlurathsrnyatcaceirodsynqdcxuimtpalotdlianiotr.no.anbtSuhuostelvwye(oourthkr??eecdup??rxioca1b)m=loep2mflhebo=iinnu0pmdawagethyrii2cxc1fnodforpimytioeusfnrotrhoenxtri=bguohet3k.sw0(dhFei).cin=Edxw0ptehlaienixnrplwasrihuntalet(sda)wpnewhiictahel (8mtraixkyso)uhveandwhy.
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