1
$\begingroup$

$A,B$ are (finite) subsets in the vector space $V$ over the field $F$.

Prove or disprove the following:

$A\bigcap B= \emptyset \ \Rightarrow spA \bigcap sp B=\{ \vec0\}$

I understand that if both sets doesn't have any element in common then the only common vector would be the zero vector, otherwise they aren't subspaces of V but I don't really know where to start on how to prove it. Any help would be appreciated.

$\endgroup$
  • 4
    $\begingroup$ What if $A=\{\vec{v}\}$ and $B=\{2\vec{v}\}$ for $\vec{v} \neq \vec{0}$? $\endgroup$ – user35603 Dec 4 '13 at 13:44
  • $\begingroup$ I think you have to disprove it. $\endgroup$ – derivative Dec 4 '13 at 13:45
1
$\begingroup$

This is not true. Take $\Bbb R$ as $\Bbb R$-vector space and $A = \{1\}, B = \{2\}$. Then $\text{span } A = \Bbb R = \text{span } B$ over $\Bbb R$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.