In linear algebra, the dimension of a subspace is the number of linearly independent vectors that span the subspace. To solve for the dimension of a subspace, we can use the following steps:
- Find a basis for the subspace.
- The number of vectors in the basis is the dimension of the subspace.
For example, consider the subspace of R^3 spanned by the vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1). These vectors are linearly independent, so they form a basis for the subspace. Therefore, the dimension of the subspace is 3.
