Final answer:
A set of vectors is linearly independent if none of the vectors in the set can be expressed as a linear combination of the others. If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent.
Step-by-step explanation:
In linear algebra, a set of vectors is linearly independent if none of the vectors in the set can be expressed as a linear combination of the others. If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent. This is because if the set contained more vectors than entries in the vectors, it would be possible to find a linear dependence among the vectors.
For example, consider a set of two-dimensional vectors with three entries each:
A = [a1, a2, a3]
B = [b1, b2, b3]
If there are only two vectors in the set, say A and B, and they have three entries each, there is no way for one vector to be expressed as a linear combination of the other vector. Therefore, the set is linearly independent.