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- Politecnico di Milano
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- Energy Engineering
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- Analisi e geometria 2
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06b Determinante e rango
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LEZIONE6 - 7.3.2023 Hp[TEOREMA-SeIinversa destracdAGM.(n) Th[ alloraAeinvertibile e A1=C. DIM.C inversed.diA Ac=I equindit Ainversa sinistradiC. r(A)=m det AFOXdetcto ->IBinversadestradiC(ConGauss-Jordan)=> C èinvertibile(heinversadestrae sinistra)e C1=Ae quindiA=c TEOREMA(sel'invertibilitàdellematrici)- Sia AM (n)lesegmenticondizionisono equivalentii. Ae invertibilea destra(sinistra)inA èinvertibile in- r(A)=M is, detAto L'inversasipucalcolarecon Gauss-Jordan DETERMINANTEC RANGO Def-dataA GM.(m,m)ew MINOREd- ORDINEè ildeterminantedi ener notomatricequadratodiAdiorcinep-Es- 2 2 0 - 4 A= - 1 - 20 2 GM(3,4)I0 100 Ip=min (m,n)inquestoces pE3 p=3 2 0 2 0 3 detso- - 2 =0 I Io attoI-e F00 I 8 0 12E2= ma[21= - (1- 4)=0det- 1 - 2 0 I EldetI0 =0 - p=2 quantiroms!3.()=3.6 =18 * s-aut[oI=0es IIdet- 1 0⊥0 defI- det[i]=- 2.I0 Percess:calcolarealcunialtriminori TEOREMADI KRONECKER Ilrangodiuna matricaèl'ordinemassimo diun minorenow hull. InaltreparoleI aw minored'ordinerr(A)=rx I Snowmeo · tati iminori diordine percon meli Es.Nell'esempioprecedenter(A) =2 /verificarecon riduzionea scola). Oss.Pergarantirechetuttiiminoridi ordineparsiamonullièsufficientemostrarecheloroquellidi arch r+ 1. DIM.(I)*Tr A rediordiner war mille A =v W- I... II&.... o C PreuchamsottmatriceBottenutacancellandrighee columede non contengopivot B= T.)en suBsottometrice diV detB= P,....... Prfo
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