When a span of set of vectors is equal to span of canonical basis with the same dimension I need to clarify some linear algebra concepts;
Row vectors $[1,0,0,0],[0,1,0,0] \in R^4 $ span a subspace of dimension $2$.
And rows $[0,1,0,0] [0,0,0,1]$ as well, and I think they do not span the same subspace, but have same dimension, and I'm not sure
why is that?
When span of set of vectors is equal to span of canonical basis(which generates entire $R^2$ with the same dimension? I'm confusing the concepts, thanks for help in advance
 A: Instead consider maybe the last vector to be $(0,0,1)$ instead, so you can visualise everything in $\mathbb R^3$. The span of the first two vectors and the second vectors are both planes going through the origin (which?), but different ones. Does it seem logical to you that they both have the same dimensions (which you can imagine a little bit like size and which is exactly the number of linearly independent vectors that span the subspace) but still be different?
A: Indeed they span different subspaces. Why would you think that they span the same subspace?
Consider a simpler example that can be visualised easily. Consider $R^3$ and clearly $(1,0,0)$ and $(0,1,0)$ span the entire $xy-$plane however, $(0,1,0)$ and $(0,0,1)$ span the entire $yz-$ plane.  
Why so? It is because taking only a few basis doesn't exhaust all the cases. In this case, taking only two such as $(1,0,0)$ and $(0,1,0)$ doesn't consider the case  $(0,1,0)$ and $(0,0,1)$.
To generate a subspace, no. of linearly independent vectors should be equal to no. of basis of that subspace which is also called dimension of the subspace.
