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 

Probleme din G.M. ( Gazeta Matematica )

 
Post new topic   Reply to topic    mateforum.ro Forum Index -> Clasa a XI-a -> Algebra
View previous topic :: View next topic  
Author Message
denisilie94



Joined: 20 Mar 2011
Posts: 3
Location: Tulcea

PostPosted: Thu Mar 08, 2012 11:44 pm    Post subject: Probleme din G.M. ( Gazeta Matematica ) Reply with quote

Fie X,Y∈M2(ℂ) cu proprietatea ca 2Y^{2}=YX-XY. Sa se arate ca : Y^{2}=O2.
Back to top
View user's profile Send private message Yahoo Messenger
Tibi1



Joined: 27 Jun 2013
Posts: 1

PostPosted: Thu Jun 27, 2013 10:36 pm    Post subject: Reply with quote

tr(Y^2)=0 si deci Y^4=-det(Y^2)I2. Inmultim relatia initiala la stanga(dreapta) cu X si le adunam si avem 4Y^3=Y^2X-XY^2. Inmultim aceasta relatie stanga(dreapta) cu Y^2 si le adunam si obtinem 8Y^5=Y^4X-XY^4=O2 si de aici rezulta Y^2=O_{2}.
Back to top
View user's profile Send private message
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