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