Yes, you've gotten the answer already. merely refers to the 4 dimensional vector space with each vector component being in the reals. Each one of your rows or columns is a point in that space.
My question asks me to consider a matrix A
Then find a basis for the nullspace of A, and hence then dimension of the nullspace;
which I find to be .
Since there are two basis vectors the dimension is 2, right?
My problem then is "Using the rank-nullity theorem or otherwise, determine the dimension of the subspace of R^{4} spanned by the four columns of A".
R-N states that dimension null = #cols - rank...
So dimension null =2 , #cols = 4, so I'm guessing rank = 2...
I'm confused by the mention of the "dimension of the subspace of R^{4}" though.
Is the answer they're looking for simply 2? And how ought I to phrase this to explain my answer, rather than merely subtracting one number from another?
Thanks in advance