(adsbygoogle = window.adsbygoogle || []).push({}); concept of a "basis" for a vector space

I do not understand the concept of a "basis" for a vector space.

Here's an example from my practice final exam:

Suppose U and V are subspaces of the real vector space W and {u1} is a basis for U and {v1} is a basis for V. If U intersection V = {0} show that {u1, v1} is a linearly independent set it W.

I probably need additional help with this example, but if someone could explain a "basis" to me in terms of this example I would greatly appreciate it.

Thanks.

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# Concept of a basis for a vector space

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