Given that the set of all 3*2 matrices with complex elements is a complex vector space, with the usual definitions of addition and scalr multiplication of matrices, what is its dimension?
Are the following subsets subspaces?
1) The set of 3*2 with real entries
2) The set of matrices with first row (0,0)
3) The set of matrices with first row (1,1)
I understand the dimension of a vector space is the number of vectros in any basis for the space, ie the number of coordinates necessary to specify any vector. How do I find out what its dimension is?