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Determinanti

 
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Silvian
Euclid


Joined: 19 Aug 2011
Posts: 12
Location: Bucuresti

PostPosted: Sun Nov 06, 2011 1:06 am    Post subject: Determinanti Reply with quote

Se considera matricea A=
(1 1 1 )
(1 1 1)
(1 1 1)
Aratati ca A+A^2+......A^2001=3^2001 -1/2 ORI A

Demonstrati ca daca avem 3 progresii aritmetice de cate trei termeni a,b,c respectiv x,y,z si u,v,w ,atunci determinantul matricei
(a b c)
(x y z)
(u v w)
este egal cu 0
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Beniamin Bogosel
Co-admin


Joined: 07 Mar 2008
Posts: 760
Location: Chambery, Franta

PostPosted: Sun Nov 06, 2011 11:40 pm    Post subject: Reply with quote

La prima problema, daca vei calcula A^2 vei obtine 3A. De aici prin inductie problema se termina usor.

Pentru cea de-a doua problema, gandeste-te eventual sa scazi coloanele intre ele. Deoarece ai progresii aritmetice vei obtine doua coloane constante, si astfel determinantul e zero.
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