I realize that you already figured this out, but if you look at what I said, I didn't say that one of the functions was a multiple of another. I said that one function was a linear combination of the other two.Dustinsfl said:
A subspace is a subset of a vector space that follows the same rules and operations as the vector space. It is closed under addition and scalar multiplication, and contains the zero vector.
The dimension of a subspace is determined by the number of linearly independent vectors that span the subspace. This is also known as the number of basis vectors in the subspace.
Yes, a subspace can have a dimension of zero if it only contains the zero vector. This means that the subspace is trivial, or has no directionality.
The dimension of a subspace is always less than or equal to the dimension of its vector space. This is because a subspace is a subset of the vector space and cannot contain more dimensions than the vector space itself.
The dimension of a subspace is important in linear algebra as it helps determine the number of free variables in a system of linear equations and the rank of a matrix. It is also used in finding the null space and column space of a matrix.