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Rangul unei matrice

Rangul unei matrice. Fie A apartine M cu m linii si n coloane o matrice nenula ; Spunem ca matricea A are rangul r si scriem rang A=r, daca A are un minor nenul de ordin r , iar toti minorii mai mari decat r(daca exista) sunt nuli .

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Rangul unei matrice

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  1. Ranguluneimatrice Fie A apartine M cu m linii si n coloane o matricenenula; Spunemcamatricea A are rangul r si scriemrang A=r, daca A are un minornenul de ordin r , iar toti minoriimai mari decat r(daca exista) suntnuli. Daca A este matricea nula , convenimsaspunem k matricea are rangul 0.adica rang (0m,n)=0.

  2. TeoremaFie A diferit de 0m,n o matrice;Numarul natural r esterangulmatricei A dacasinumaidacaexista un minor de ordin r al luiA,nenul, iartotiminori de r+1 (dacaexista) suntnuli.

  3. A= min{2,2}=2 , Rezolvarepartialafisa 5 =26 –(-18) =26 -18 = 8 ≠0 => rangA =2 min{2,2}=2 , 1.b) A = 1.a) = 6-10 =-4 ≠0 => rangA =2 1.C) A= = -15 +2 =-13≠0 => rangA =2 • d) A= cum detA =0 si =1≠0 => rangA =1

  4. A= min{2,3)=2 Minor de ordin 2 r=2 Fisa 5 d = =-1 ≠0 => rangA =2 • A= min{3,2)=2 Minor de ordin r=2 2) 3) d = =-2 ≠0 => rangA =2

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