Linear Algebra 2 Quick questions regarding my understanding of isomorphism

Question

I know the definition of isomorphism but can you provide me two isomorphic subspaces of $\mathbb R^2$ that are not identical, and an example of a set that spans a subspace of $\mathbb R^3$ but is not a basis for that subspace?

Answer 1

You mean like $\mathbb R \times \{0\}$ and $\{0\}\times \mathbb R$?

And $\operatorname{Span}\{(1,0,0),(0,1,0),(1,1,0)\}=\mathbb R\times\mathbb R\times \{0\}$, but that spanning set is not a basis for that subspace of $\mathbb R^3$ since it is not linearly independent.

These examples are trivial.