Hi,

Just hoping that someone can help me better understand the dimension of a subspaces. To start, I will show this paragraph:

So there's a matrix that has 3 columns and 4 rows. I don't understand, fundamentally speaking, why the matrix would be a 2-dimensional subspace of R^4. I understand why it would be a subspace of R^4 (since each column has 4 components and therefore lies within the vector space of R^4), but I don't understand why it would be a 2-dimensional subspace. I know that the number of pivots indicates the dimension of the subspace (in this case there would be 2 pivots) - but I don't understand WHY this is the case. The mechanics of determining the subspace dimension is simple and what I want to understand is the theory behind the dimension of a subspace. I hope this makes sense.

Please please help. I've been trying to wrap my head around this idea for hours :'(

- otownsend