mateforum.ro Forum Index mateforum.ro

 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

matricea A la puterea n (cu binoumul lui Newton)

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Algebra
View previous topic :: View next topic  
Author Message
tovy



Joined: 21 Nov 2011
Posts: 2

PostPosted: Tue Nov 29, 2011 7:43 pm    Post subject: matricea A la puterea n (cu binoumul lui Newton) Reply with quote

vreau sa calculez A la n

A=(-1 1 1)
(1 -1 1)
(1 1 -1)
Back to top
View user's profile Send private message
Beniamin Bogosel
Co-admin


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

PostPosted: Tue Nov 29, 2011 11:16 pm    Post subject: Reply with quote

Pai chiar tu spui ca vrei sa calculezi matricea la puterea n cu binomul lui Newton. Pentru asta trebuie sa scrii matricea A ca suma de doua matrici "stas" pentru care sa poti estima usor puterile lor, si apoi sa aplici binomul. Pentru asta, nu e greu de observat ca A=B-2I unde B=\begin{pmatrix} 1&1&1 \\ 1&1&1 \\ 1&1&1 \end{pmatrix} si I este matricea identitate.
Se poate observa usor ca B^2=3B, si de aici, prin inductie afli usor forma lui  B^n. Matricea unitate la orice putere e tot matricea unitate. Mai departe aplici binomul si gata. Daca nu iti iese, te mai ajut, dar ar trebui sa te chinui si tu un pic cu ea ca nu e mare lucru, si iese Wink
_________________
Yesterday is history,
Tomorow is a mistery,
But today is a gift.
That's why it's called present. Smile

Blog
Back to top
View user's profile Send private message Visit poster's website Yahoo Messenger
Display posts from previous:   
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Algebra All times are GMT + 2 Hours
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum



Powered by phpBB © 2001, 2005 phpBB Group