A subspace is a subset of a vector space that satisfies three properties: closure under addition, closure under scalar multiplication, and contains the zero vector.
To determine if a set is a subspace of R^4, you must check if it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector. If all three properties are satisfied, then the set is a subspace of R^4.
No, a subspace of R^4 can only have a maximum of four dimensions since R^4 is a four-dimensional vector space. Any set with more than four dimensions cannot be a subset of R^4.
Yes, the empty set is considered a subspace of R^4 since it satisfies the three properties of a subspace. It is closed under addition and scalar multiplication, and it contains the zero vector.
Yes, a line or a plane can be a subspace of R^4 as long as it satisfies the three properties of a subspace. For example, the x-axis or the xy-plane can be considered subspaces of R^4.