vector spaces, linear independence and functions
So here is the question. This is part of an essay. this is in the context also of the four fundamental subspaces. Obviously i'm not asking for essays but im just confused on this as a whole:
elaborate on how sets of functions and sets of matrices (say 2x2 matrices) can satisfy the definition of a vector space. Discuss what might change when the vectors themselves are not n-tuples. what would it mean for a set of 5 matrices to be considered linearly independent. What about a set of 4 functions?
im confused on the difference of functions and matrices they are talking about here. are they one in the same?? so for a vector space, it must be a subspace of that vector space? so when the vectors are not n-tuples (does that mean not a square matrix?), so does the space of the vectors change as well? im sorry if im not making sense im really confused here we have a teacher that doesnt make much sense and speaks poor english so any help would be great!!!