Let W be a subspace of Vn of dimension k. Prove: Every basis of W has k vectors. [Hint: Show first that no basis can have more than k vectors. Next suppose that a basis has fewer than k vectors. By completing the given basis of k vectors to a basis for Vn, show that one could then obtain a basis for Vn of less than n vectors.]
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.