[問題]一個線代的問題..

[AaronSWAT (Aaron)]

在課本215頁的Theorem 4.5 提到:

Let V be a subspce of Rn having dimension k. Then any two of the following
conditions about a subset S of V imply that S is a basis for V.
    (a) S is lin. independent.
    (b) S is a spanning set for V.
    (c) S contains exactly k vectors

所以只要滿足上面任一兩個 那S就是V的一個basis


可是216頁又提出三個判斷basis的步驟:
   (i) Show that B is contained in V.
  (ii) Show that B is lin. independent.
 (iii) Compute the dimension of V, and confirm that the number of vectors in
       B equals dim V.

  第二和第三步驟 就已經和前一頁的(a),(c)符合   為什麼要有步驟一啊??

  請指導...(拯救XD)

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推 timrau:(i)是在驗證定理的前提正確
推 tsukasa2004:你注意一下定理的最後一行 about a "subset"
→ tsukasa2004:S of V 所以才要檢查(i)