A subspace in linear algebra is a subset of a vector space that satisfies all of the properties of a vector space. This means that it must be closed under vector addition and scalar multiplication, and it must contain the zero vector.
To determine if a set is a subspace, you must check if it satisfies the three properties of a vector space: closure under vector addition, closure under scalar multiplication, and the presence of the zero vector. If all three properties are met, then the set is a subspace.
A subspace is a subset of a vector space that satisfies all of the properties of a vector space. A span, on the other hand, is the set of all possible linear combinations of a given set of vectors. In other words, a subspace is a subset of a vector space, while a span is a collection of vectors within a vector space.
Yes, a subspace can have more than one basis. A basis is a set of linearly independent vectors that span the entire subspace. Since there can be multiple sets of linearly independent vectors that span the same subspace, there can be more than one basis for a subspace.
The dimension of a subspace is equal to the number of vectors in its basis. Therefore, to find the dimension of a subspace, you can find a set of linearly independent vectors that span the subspace and count the number of vectors in that set.