Why is determinant function continuous? | Study.com

Answer to: Why is determinant function continuous? Lets define a function in {eq}n^2 {/eq} variables. {eq}f(a_{11},a_{12},...,a_{1n}, .... , a_{n1}, ...,... forTeachers forSchools forWorkingScholars® forCollegeCredit LogIn SignUp Menu forWorkingScholars® forCollegeCredit Plans Plans Courses Courses FindCoursesbySubject Science Math Business Psychology History English SocialScience Humanities Spanish ProfessionalDevelopment ByEducationLevel College HighSchool MiddleSchool TestPrep PopularTests… PopularTests SAT ACT TOEFL GMAT GRE CLEP GED ASVAB RealEstate TeacherCertification… TeacherCertification AEPA CEOE CSET/CBEST FTCE GACE ILTS MTEL MTLE MTTC MoGEA/MEGA NES NYSTCE OAE Praxis RICA TExES VCLA WEST Nursing… NursingTests HESI TEAS NCLEX PAXRN CNE OtherTests… OtherTests AP ASCP ASWB Accuplacer CHSPE CTEL DSST Finance FSA HSPT ISEE MBLEx NCE PERT PHR SHSAT TASC TECEP UExcel Exploreover 4,600 videocourses BrowseAllCourses SAT ACT TOEFL GMAT GRE CLEP GED ASVAB RealEstate AEPA CEOE CSET/CBEST FTCE GACE ILTS MTEL MTLE MTTC MoGEA/MEGA NES NYSTCE OAE Praxis RICA TExES VCLA WEST HESI TEAS NCLEX PAXRN CNE AP ASCP ASWB Accuplacer CHSPE CTEL DSST Finance FSA HSPT ISEE MBLEx NCE PERT PHR SHSAT TASC TECEP UExcel Credit Credit CreditOptions CreditOptions OnlineCollegeCredit HighSchool&GED CertificatesofCompletion HowitWorks TransferCredit TransferCredit AllTransferCredit FindYourSchool CollegeCoursesforCredit TransferringCredit HowItWorks EarnTransferableCredit&GetyourDegreefast Learnmore ContactSupport Question: Whyisdeterminantfunctioncontinuous? TheDeterminantofaMatrix: Let{eq}A=(a_{ij})\inM_n(\mathbb{R}) {/eq}besomematrix. Wedefinethedeterminantofthematrixinthefollowingway: {eq}det~A=\sum_{\sigma\inS_n}sgn(\sigma)a_{1\sigma(1)}a_{2\sigma(2)}...a_{n\sigma(n)} {/eq} Inthisdefinition{eq}S_n {/eq}isthesetofallpermutationoftheset{eq}\{1,2,...,n\} {/eq}and{eq}sgn(\sigma) {/eq}issignofthepermutation. Itisalsoimportanttoknowthatpolynomialsarecontinuousandthatthesumandproductoftwocontinuousfunctionsarealsocontinuous. AnswerandExplanation: 1 BecomeaStudy.commembertounlockthisanswer! Create your account Viewthisanswer Letsdefineafunctionin{eq}n^2 {/eq}variables. {eq}f(a_{11},a_{12},...,a_{1n},....,a_{n1},...,a_{nn})=\sum_{\sigma\inS_n}sgn(\sigma)... Seefullanswerbelow. BecomeamemberandunlockallStudy Answers Tryitrisk-freefor30days Tryitrisk-free Askaquestion Ourexpertscanansweryourtoughhomeworkandstudyquestions. Askaquestion Askaquestion SearchAnswers Learnmoreaboutthistopic: GetaccesstothisvideoandourentireQ&Alibrary Tryitrisk-free HowtoTakeaDeterminantofaMatrix from Chapter2 /Lesson2 37K Explorethedeterminantofamatrix,whichiswidelyusedinlinearalgebra.Understandhowtofindthedeterminantofamatrixwithdeterminantrulesandlearntodeterminetheorderofthematrix. RelatedtothisQuestion RelatedAnswers RelatedLessons RelatedCourses FindtheJacobianforthefollowingchangeof... FindtheJacobianofthetransformation... WhenisamatrixPinvertible,andhowto... 1.)Withoutcomputing3AA^T,find|3AA^T|for... Findthedeterminantofeachofthefollowing... LetA=\begin{bmatrix}0&1\\2&1\\1&-1... (a)UseGaussianEliminationwithoutpivoting... (u,v)\rightarrow(u^{2}/v,v^{2}/u)Findthe... UseCramer'sruletosolvethelinearsystem... Evaluatethedeterminantbycofactorexpansion.... Findthedeterminantofthematrix[-50-21... ComputethedeterminantofAusingrow... Giventhat|111143123|=4,find|246... 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