The span of a set of 3D vectors refers to the set of all possible linear combinations of those vectors. In other words, it is the space that can be reached by scaling and adding together the vectors in the set.
To calculate the span of a set of 3D vectors, you can use the Gaussian elimination method to reduce the set to its row-echelon form. The number of non-zero rows in the reduced matrix will correspond to the dimension of the span.
The span of a set of 3D vectors represents the subspace that is spanned or generated by those vectors. This subspace can be thought of as a plane, line, or point in 3D space depending on the dimension of the span.
Yes, the span of a set of 3D vectors can be infinite if the vectors are linearly independent. This means that there are an infinite number of possible combinations of the vectors that can be used to reach any point in the span.
The span of a set of 3D vectors is closely related to linear independence. If the vectors in the set are linearly independent, then the span will be a unique subspace in 3D space. However, if the vectors are linearly dependent, then the span will be a lower-dimensional subspace or even a single point.