subset U subset is NOT subspace of Superset?

Sep 2009
1
0
Hello,
I have an assignment due tomorrow, and Im stuck at this problem:

Let V be a vector space over any field F, and W1 and W2 be two subspaces of V.
b) Give examples for V, W1, W2 such that W1 U W2 is NOT a subspace of V.

Any ideas?
 
Jun 2009
1,266
498
Canada
In \(\displaystyle \mathbb{R}^2\) : \(\displaystyle span\{(1,0)\} \cup span\{(0,1)\}\) is not a subspace - for instance it does not contain \(\displaystyle (1,0)+(0,1)\)