mat261_calisma_sorulari_3.pdf - C \u00b8 ALIS \u00b8 MA SORULARI III Ders MAT 261 Konu Vekt\u00a8or Uzaylar\u0131 1 A\u00b8sa\u02d8g\u0131daki k\u00a8 umeler verilen toplama ve skaler

mat261_calisma_sorulari_3.pdf - C ¸ ALIS ¸ MA SORULARI...

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C ¸ ALIS ¸MA SORULARI III Ders: MAT 261 Konu: Vekt¨ or Uzayları 1. A¸ sa˘gıdaki k¨umeler, verilen toplama ve skaler ¸carpma i¸ slemlerine g¨ore vekt¨or uzayı olur mu? Olmazsa vekt¨ or uzayı tanımındaki ko¸ sullardan hangileri sa˘glanmaz? A¸cıklayınız. (a) V = pozitif reel sayılar k¨umesi, i¸ slemler: bilinen (yani standart) toplama ve skalerle ¸carpma i¸ slemleri, (b) V = pozitif reel sayılar k¨umesi, slemler: (toplama) x L y = xy ; (skalerle ¸carpma) α J x = x α ( α R ), (c) V = Z = Tam sayılar k¨umesi, slemler: bilinen (yani standart) toplama; (skalerle ¸carpma) α J k = b α c k ( α R , k Z , b·c : tamde˘ger fonksiyonu), (d) V = R 3 , i¸ slemler; x y z L x 0 y 0 z 0 = x + x 0 y + y 0 0 , α J x y z = 3 y z (e) V = R 2 ’de x y , y 0 ko¸ sulunu sa˘glayan k¨ume ve bilinen toplama ve skaler ¸carpma i¸ slemleri. 2. R 2 × 2 ’de a b c d , ab = 0 ¸ seklinde elemanlara sahip bir k¨ume matris toplam ve skaler ¸carpma i¸ slemlerine g¨ore vekt¨or uzayı mıdır? Neden? 3. R reel sayılar k¨umesinin x M y = min { x, y } , α K x = αx slemlerine g¨ore vekt¨ or uzayı olu¸
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