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Matrice inversabila

 
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Silvian
Euclid


Joined: 19 Aug 2011
Posts: 12
Location: Bucuresti

PostPosted: Wed Nov 23, 2011 12:15 am    Post subject: Matrice inversabila Reply with quote

Daca A e Mn este nesingulara si daca AX=In,sa se arate ca XA=In
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Alin
Euclid


Joined: 27 Mar 2010
Posts: 16

PostPosted: Wed Nov 23, 2011 5:30 pm    Post subject: Reply with quote

Nu prea spui nimic despre natura matricei X.
Insa, daca A este nesingulara atunci \det(A)\ne 0 deci exista B astfel incat AB=I_n, fie B=A^{-1}.

Din relatia : AX=I_n \Longleftrightarrow A^{-1}(AX)=A^{-1} \Longleftrightarrow X=A^{-1} \Longleftrightarrow XA=A^{-1}A \Longleftrightarrow XA=I_n.
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