Prove the following:
A system of linear equationsAx = b with m < n either has no solution or has several different solutions.
A system of linear equations Ax = b where A has rank m always has a solution.
I think I'm making a little bit of headway but some help would be much appreciated
Suppose A has rank n, that is A is invertable. Then has a unique solution by uniqueness of the matrix-inverse.
If A has rank m < n then it is row-equivalent with a matrix with at least one row zero's, say row i, . Suppose it does have a solution . Then for any choice of we have that is a solution.