(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove or disprove this with counter example:

Let U,V be subspaces of R^n and let B = {v1, v2,...,vr} be a basis of U. If B is a subset of V, then U is a subset of V.

2. Relevant equations

U and V are subspaces so

1. zero vector is contained in them

2. u1 + u2 is in U and v1 + v2 is in V when u1 and u2 are already in U and v1 and v2 are in V

3. au1 is in U and av1 is in V when a is in R

3. The attempt at a solution

Since B is a basis of U, B is a linearly independent spanning set of U and all of the elements of B are in U.

Since B is a subset of V, all of the elements of B are in V.

However this does no guarentee that all the elements of U are in V...Correct?

Well assuming that that is correct, I am having the hardest time finding a counter example.

At first I was just taking a set of vectors and calling that U. Finding the basis of that set of vectors and calling it B. And then creating another random set of vectors that contained the elements that were in B but left out the ones in U. But then I realized that U and V are subspaces so I got lost.

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# Homework Help: Subspace and basis help

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