The span of a vector is the set of all possible linear combinations of that vector. In other words, it is the space that can be created by scaling and adding the vector in different directions.
To create vectors for the span, you can use a linear combination of existing vectors. This means multiplying each vector by a scalar (a number) and then adding them together. The resulting vector will be in the span of the original vectors.
The span is important in linear algebra because it helps us understand the dimension and structure of a vector space. It also allows us to determine whether a vector is a linear combination of other vectors or not.
Yes, a set of vectors can have an infinite span. This means that there are an infinite number of possible linear combinations of the vectors, resulting in an infinite number of vectors in the span.
To determine if a vector is in the span of a set of vectors, you can use the process of elimination. If you can find a linear combination of the set of vectors that equals the given vector, then it is in the span. If not, then it is not in the span.