The span is considered the smallest containing subspace because every other subspace containing those vectors must also contain their span. Since the span consists of all linear combinations, any subspace closed under addition and scalar multiplication that includes the original vectors must include all their combinations.
Conditions: The collection of vectors is fixed.; We are comparing subspaces that contain this collection.
The span is considered the smallest containing subspace because every other subspace containing those vectors must also contain their span. Since the span consists of all linear combinations, any subspace closed under addition and scalar multiplication that includes the original vectors must include all their combinations.
Conditions: The collection of vectors is fixed.; We are comparing subspaces that contain this collection.
The span of a collection consists of all its linear combinations. It is a subspace containing the collection, and every other subspace containing those vectors must also contain their span.
Conditions: The collection consists of one or more vectors.; Linear combinations involve scalar multiplication and vector addition.
The span of a collection consists of all its linear combinations. It is a subspace containing the collection, and every other subspace containing those vectors must also contain their span.
Conditions: The collection consists of one or more vectors.; Linear combinations involve scalar multiplication and vector addition.