每週問題 August 15, 2016

Posted on 08/15/2016 by ccjou

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)。

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1 Response to 每週問題 August 15, 2016

  1. Peter Chan says:
    08/15/2016 at 4:41 pm

    Simple and direct proof

    Reply

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