Math Help - union and intersection of bases

1. union and intersection of bases

I know thsi may seem very simple but i at a loss,

if i have two bases S and T
with the union being R and the intersection being Y

can i say that R is linearluy independent and Y is not??????

also if anyen cold give me a defintion for the union of vectorspaces it would be much appreciated!!!!!

2. Originally Posted by calculusgeek
with the union being R and the intersection being Y
The union is not necessary linearly independent.
Let $S = \{ \bold{i},\bold{j}\}$ and $T = \{ 2\bold{i},2\bold{j}\}$ as basis for $\mathbb{R}^2$.
Clearly, $S\cup T$ is not linearly independent.

Now if $S,T$ are basis and $S\cap T$ is non-empty then it is non-empty subset of a linearly independent set therefore it itself must be linearly independent.