03-12-2014 11:14 AM
Did you mis-state the problem? Usually A and b are known and you need to find x.
As you've stated it, the problem has infinitely many solutions when x is not identically zero.
Since x is not all zeros, there is some element x_i which is nonzero. Construct the matrix A that is zero everywhere except for the i_th column, where it has the value b/x_i.
x = T(4:0);
b = T(1:3);
i=1; /* for this problem x is nonzero */
A = j(nrow(b), nrow(x), 0);
A[,i] = b/x;
diff = A*x-b; /* compute A*x - b */