Which of the following best defines a subspace in linear algebra?

A subspace in linear algebra is indeed defined as a subset of a vector space that is also a vector space. This definition encompasses several critical properties that a subspace must satisfy:

1. Containment of the Zero Vector: A subspace must include the zero vector of the larger vector space it belongs to. This is essential because every vector space must contain the zero vector.

2. Closure Under Addition: If you take any two vectors in the subspace and add them together, their sum must also be in the subspace. This property ensures that the operations of vector addition remain valid within the subspace.

3. Closure Under Scalar Multiplication: If you take any vector in the subspace and multiply it by a scalar (a real number), the resulting product must also be part of the subspace. This preserves the linear structure of the vectors.

These conditions confirm that a subspace not only retains the properties of the larger vector space, but also supports all operations defined within that vector space, effectively allowing it to function independently as a vector space in its own right.

The other options do not fulfill the necessary criteria to define a subspace accurately. For example, a space containing only zero vectors does not represent all