每週問題 August 15, 2016

為甚麼 \{\mathbf{0}\} 是一個線性相關集?

Let S=\{\mathbf{0}\} be the set containing only the zero vector.
(a) Explain why S must be linearly dependent.
(b) Explain why the empty set is a basis for S.

 
參考解答:

(a) 存在非零數 c 使得 c\,\mathbf{0}=\mathbf{0},根據定義,\{\mathbf{0}\} 是一個線性相關集。

(b) 對於子空間 S=\{\mathbf{0}\}, 不存在非空的線性獨立生成集,故 S=\hbox{span}(\emptyset)

This entry was posted in pow 向量空間, 每週問題 and tagged . Bookmark the permalink.

1 Response to 每週問題 August 15, 2016

  1. Peter Chan says:

    Simple and direct proof

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