[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/579a32f9a3a085a219a94dffe30b9530.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/579a32f9a3a085a219a94dffe30b9530.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/579a32f9a3a085a219a94dffe30b9530.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/579a32f9a3a085a219a94dffe30b9530.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/579a32f9a3a085a219a94dffe30b9530.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/b89b78ec78ad2984a426aa2f859c20a3.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/b89b78ec78ad2984a426aa2f859c20a3.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/b89b78ec78ad2984a426aa2f859c20a3.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/b89b78ec78ad2984a426aa2f859c20a3.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/b89b78ec78ad2984a426aa2f859c20a3.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/b89b78ec78ad2984a426aa2f859c20a3.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/b89b78ec78ad2984a426aa2f859c20a3.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/b89b78ec78ad2984a426aa2f859c20a3.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/b89b78ec78ad2984a426aa2f859c20a3.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/b89b78ec78ad2984a426aa2f859c20a3.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/b89b78ec78ad2984a426aa2f859c20a3.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/b89b78ec78ad2984a426aa2f859c20a3.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/b89b78ec78ad2984a426aa2f859c20a3.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/b89b78ec78ad2984a426aa2f859c20a3.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/b89b78ec78ad2984a426aa2f859c20a3.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/b89b78ec78ad2984a426aa2f859c20a3.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/b89b78ec78ad2984a426aa2f859c20a3.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/b89b78ec78ad2984a426aa2f859c20a3.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/b89b78ec78ad2984a426aa2f859c20a3.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/b89b78ec78ad2984a426aa2f859c20a3.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/b89b78ec78ad2984a426aa2f859c20a3.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/b89b78ec78ad2984a426aa2f859c20a3.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/b89b78ec78ad2984a426aa2f859c20a3.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/b89b78ec78ad2984a426aa2f859c20a3.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/b89b78ec78ad2984a426aa2f859c20a3.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 300: unlink(/7bcefa13872ba4706540bf387170e897.aux): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 301: unlink(/7bcefa13872ba4706540bf387170e897.log): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 302: unlink(/7bcefa13872ba4706540bf387170e897.dvi): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 303: unlink(/7bcefa13872ba4706540bf387170e897.ps): No such file or directory
[phpBB Debug] PHP Notice: in file /var/www/forum.math.uoa.gr/www/latexrender/class.latexrender.php on line 304: unlink(/7bcefa13872ba4706540bf387170e897.png): No such file or directory
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4312: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4314: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4315: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4316: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
forum.math.uoa.gr • Προβολή θέματος - αποδεικτική άσκηση γραμμική άλγεβρα - ερώτηση

forum.math.uoa.gr

Forum του Τμήματος Μαθηματικών
Ημερομηνία 23 Νοέμ 2017, 22:34

Όλοι οι χρόνοι είναι UTC + 2 ώρες [ DST ]




Δημιουργία νέου θέματος Απάντηση στο θέμα  [ 3 δημοσιεύσεις ] 
Συγγραφέας Μήνυμα
 Θέμα δημοσίευσης: αποδεικτική άσκηση γραμμική άλγεβρα - ερώτηση
ΔημοσίευσηΔημοσιεύτηκε: 09 Οκτ 2016, 15:02 
Χωρίς σύνδεση

Εγγραφή: 06 Οκτ 2016, 16:35
Δημοσ.: 3
Καλησπέρα , είναι ο συλλογισμός που χρησιμοποιώ, για την απόδειξη του παρακάτω , σωστός , κι αν όχι, πως αποδεικνύεται ...;
-Ας είναι x, y [unparseable or potentially dangerous latex formula] διανύσματα και I μοναδιαίος nxn πίνακας ,
δείξτε ότι :
[unparseable or potentially dangerous latex formula]
(υπ:det=ορίζουσα)

Λύση:
Η οριζουσα ενος αναστροφου πινακα ειναι ιση με την οριζουσα του ιδιου πίνακα:
[unparseable or potentially dangerous latex formula]
Άρα,
[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula] αριθμος ,η ορίζουσα ενος αριθμου ειναι ο ιδιος ο αριθμος
οριζουσα του μοναδιαιου I nxn ισούται με τη μονάδα:1
[unparseable or potentially dangerous latex formula]

Ευχαριστώ !


Κορυφή
 Προφίλ  
 
 Θέμα δημοσίευσης: Re: αποδεικτική άσκηση γραμμική άλγεβρα - ερώτηση
ΔημοσίευσηΔημοσιεύτηκε: 09 Οκτ 2016, 19:46 
Χωρίς σύνδεση
Regular Forumer

Εγγραφή: 29 Οκτ 2010, 01:19
Δημοσ.: 158
[unparseable or potentially dangerous latex formula]

η ισότητα αυτή δεν ισχύει.
Spoiler:
[unparseable or potentially dangerous latex formula]

το δεξί μέλος είναι η πρόσθεση ενός n\times n πίνακα μ έναν αριθμό(1\times 1 πίνακα), οπότε δεν είναι καλά ορισμένη.
Επίσης η συνάρτηση [unparseable or potentially dangerous latex formula] δεν είναι προσθετική.

δοκίμασε να το πάς με επαγωγή στο n.
δηλαδή αν [unparseable or potentially dangerous latex formula] και [unparseable or potentially dangerous latex formula] τότε πώς είναι ο πίνακας του οποίου θες να υπολιγίσεις την ορίζουσα και πως μπορείς να αξιοποιήσεις την επαγωγική υπόθεση;


Κορυφή
 Προφίλ  
 
 Θέμα δημοσίευσης: Re: αποδεικτική άσκηση γραμμική άλγεβρα - ερώτηση
ΔημοσίευσηΔημοσιεύτηκε: 10 Οκτ 2016, 17:16 
Χωρίς σύνδεση
Regular Forumer

Εγγραφή: 29 Οκτ 2010, 01:19
Δημοσ.: 158
[unparseable or potentially dangerous latex formula] = [unparseable or potentially dangerous latex formula] + [unparseable or potentially dangerous latex formula]=

=[unparseable or potentially dangerous latex formula]=[unparseable or potentially dangerous latex formula]=[unparseable or potentially dangerous latex formula].


Κορυφή
 Προφίλ  
 
Τελευταίες δημοσιεύσεις:  Ταξινόμηση κατά  
Δημιουργία νέου θέματος Απάντηση στο θέμα  [ 3 δημοσιεύσεις ] 

Όλοι οι χρόνοι είναι UTC + 2 ώρες [ DST ]


Μελη σε συνδεση

Μέλη σε αυτή την Δ. Συζήτηση: Δεν υπάρχουν εγγεγραμμένα μέλη και 5 επισκέπτες


Δεν μπορείτε να δημοσιεύετε νέα θέματα σε αυτή τη Δ. Συζήτηση
Δεν μπορείτε να απαντάτε σε θέματα σε αυτή τη Δ. Συζήτηση
Δεν μπορείτε να επεξεργάζεστε τις δημοσιεύσεις σας σε αυτή τη Δ. Συζήτηση
Δεν μπορείτε να διαγράφετε τις δημοσιεύσεις σας σε αυτή τη Δ. Συζήτηση

Αναζήτηση για:
Μετάβαση σε:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group