- #1
flyingpig
- 2,579
- 1
Homework Statement
Whenever LA talks about ℝn, do they mean just the n?
Ex. Let's say I have two vectors
[tex]\begin{bmatrix}1\\ 0\\ 0\end{bmatrix}\begin{bmatrix}0\\ 1\\ 0\end{bmatrix}[/tex]
Now it is tempting to say that the two vector is a basis for ℝ2.
Now my professor tells me that it isn't a basis for ℝ2 because the vectors are in ℝ3. But I don't understand why. Sure they are in ℝ3, but the two vectors span ℝ2.
Also, just to take another step further, let's say I have two vectors with three entries and I am telling you that they are linearly independent. My question is, is it a basis for ℝ2? Whenever we talk about ℝ2, do we only mean the xy-plane and not some other plane that exist in ℝn for n>2?