[理工][線代] vector space 判斷
題目出處 :
黃子嘉 題庫班 t2 p2-56 99成大應數
以下的 x 皆為 2開根號
State the definition of vector space. Show that the set
{a + bx | a,b is rational} together with the operation of addition
and mulitplication is a vector space. what is its dimension?
How about if a,b is Real numbers?
How about if a,b is integers?
Ans : 2 , 1 , 沒有定義
前兩個我沒問題
但是第三個有點沒辦法接受
直覺上來說 integer不應該要跟rational差不多辦理嗎?
解答世說 因為Z不為field, so S is not a vector space, so dim 無定義
有點搞不通他哪邊不符合fields?
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12/06 01:01, , 1F
12/06 01:01, 1F