- #1
MathewsMD
- 433
- 7
I've attached the question to this post. The answer is true, but I'm trying to figure out why.
Using Gram-Schmidt, I can only necessarily find 3 orthogonal vectors given 3 linearly independent vectors from ## R^5 ##. How then is it possible to extend this set of 3 vectors that are linearly independent to form a basis of ## R^5##? Unless I'm missing something here, the question is asking if this set can be extended to span ALL of ## R^5 ## (i.e. a basis of this space) and not just a subspace, correct? How exactly can 3 vectors do this? I believe recalling an analog to the cross product in ##R^5## but we surely did not cover this in our class. Any help would be greatly appreciated!
Using Gram-Schmidt, I can only necessarily find 3 orthogonal vectors given 3 linearly independent vectors from ## R^5 ##. How then is it possible to extend this set of 3 vectors that are linearly independent to form a basis of ## R^5##? Unless I'm missing something here, the question is asking if this set can be extended to span ALL of ## R^5 ## (i.e. a basis of this space) and not just a subspace, correct? How exactly can 3 vectors do this? I believe recalling an analog to the cross product in ##R^5## but we surely did not cover this in our class. Any help would be greatly appreciated!