Θέματα Διακριτά...

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  • 8/2/2019 1 [Feb2012]

    1/8

    D i a k r i t M a j h m a t i k I

    F l o r e n t a B l b h

    2 F e b r o u a r o u 2 0 1 2

    J E M A T A

    1 . a ) M e p s o u c t r p o u c m p o r o m e n a t o p o j e t s o u m e 1 9 b i b l a M a j h m a t i k n , 1 6 b i b l a

    Q h m e a c , 1 1 b i b l a B i o l o g a c k a i 7 b i b l a F u s i k c s e m a b i b l i o j k h t s i s t e l a t a

    b i b l a k j e t o m a n a e n a i m a z ?

    b ) P s e c e n a i o i l s e i c t h c e x s w s h c + + + = 21 p o u , , , a k r a i o i , t a n

    ( a ) , , , 0

    ( b ) , , , > 0 ( 2 . 5 m )

    2 . a ) N a b r e j e h g e n n t r i a s u n r t h s h t h c a k o l o u j a c 0 1, 1 2, 2 3, . . .

    b ) M e p s o u c t r p o u c m p o r o m e n a e p i l x o u m e 2r

    m p l e c a p n a s w r m e k k k i n e c k a i

    l e u k c , t a n j l o u m e n a q o u m e r t i o a r i j m l e u k n ? ( 2 . 5 m )

    3 . a ) N a l u j e h ar 5ar1 + 6ar2 = 2

    r + r m e a0 = 1 k a i a1 = 1

    b ) N a u p o l o g i s t e h o r z o u s a :

    An,n =

    4 2 0 0 0

    2 4 2 0 0

    0 2 4 2 0

    0 0 2 4 0.

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    0 0 0 2 4

    ( 3 m )

    4 . P s e c s e i r c t w n 1 0 a r i j m n m p o r o m e n a k a t a s k e u s o u m e q r h s i m o p o i n t a c t o u c a r i j m o c

    4, 5, 6, 7, 8 t a n p r p e i n a q r h s i m o p o i s o u m e t o u l q i s t o n m a f o r t o u c a r i j m o c

    4, 7, 8?

    ( 1 m )

    5 . P s e c d i a f o r e t i k c m e t a x t o u c s u m b o l o s e i r c m k o u c 3 m p o r o m e n a k a t a s k e u s o u m e a p

    s p r e c , m p l e k a i k k k i n e c q n t r e c ?

    ( 1 m )

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