What does it mean if a vector can be represented as a linear combination of other vectors?

When a vector can be represented as a linear combination of other vectors, it means that the vector can be formed by taking those other vectors and multiplying them by scalar coefficients, then summing the results. This concept is directly related to the notion of a "span," which is the set of all possible linear combinations of a given set of vectors.

If a vector lies within the span of a set of vectors, it implies that you can express it as a combination of the vectors in that set. Thus, the vector being discussed in this scenario is indeed part of that span, confirming the correctness of the chosen answer.

The idea of being outside the span would suggest that the vector cannot be formed in such a manner, contradicting the premise of the question. Similarly, linear independence relates to a different concept where none of the vectors in a given set can be expressed as a linear combination of the others. Lastly, describing a vector as a scalar multiple pertains specifically to one vector being a scaled version of another, which does not capture the broader context of linear combinations involving potentially multiple vectors.