Final answer:
True. Every linearly independent set of vectors is a basis for some subspace.
Step-by-step explanation:
The statement is true. Every linearly independent set of vectors is indeed a basis for some subspace.
A set of vectors is linearly independent if there is no non-trivial linear combination of the vectors that equals the zero vector. In other words, the only coefficients that can make the sum of the vectors equal to the zero vector are all zero.
A basis for a subspace is a set of vectors that spans the subspace and is linearly independent. If a set of vectors is linearly independent, it means that it can be used to generate any vector within the subspace through linear combinations.
Therefore, every linearly independent set of vectors can be considered as a basis for the subspace it spans. This is because the set provides a sufficient number of vectors and they are linearly independent, allowing us to represent any vector within the subspace.