Question

How do you find is a vector b is in the span of a set of linear equations?

Answer 1

The most simple way: find the rank of the matrix made up of the spanning vectors. If the matrix is of the same rank as the length of the vector b in question, you know the vector b is in the span.

This is an ad-hoc method if you are checking with a computer in, say, Matlab.

More information can be found at: http://en.wikipedia.org/wiki/Linear_span