I have a few true/false/depends questions. If a subspace of R^n has a basis consisting of 5 vectors then n is greater than equal to 5. I say it's true because 5 linearly independent vectors span R^5. Is that correct? If the rank of a 6x7 matrix A is 3 then A^T has 5 linearly independent column vectors. I am not sure on this. Any help would be nice.