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Fact #1

An nxn linear system Ax=b has a unique solution if
and only if A is nonsingular.

Fact #2

An mxn (where m .ne. n) linear system Ax=b has either 
no solution (termed "inconsistent") or an infinite number 
of solutions.

Fact #3

The best you can do is a "least squares" solution.
Notation: A' = transpose of A
          A^ = inverse of A 
          ||x|| = Euclidean norm of the vector x
Say you want to solve Ax=b where A is nx3
==> A'Ax = A'b  (these are the "normal equations")
    If the columns of A are linearly independent, then the
    3x3 matrix A'A is nonsingular.
==> x = (A'A)^A'b, i.e., x is the unique solution to the 
    normal equations and the unique least squares solution
    to Ax=b.
    
Definition of a least squares solution:
 x is least squares solution if and only if
 ||Ax - b|| .le. ||z - b|| for all other vectors z.

You may want to refer to "Introduction to Matrix 
Computations" by Gilbert Stewart or some other text
on numerical linear algebra.

Hope this helps.

K. Banerjee