I get the same (wrong) result as you. Thats what happens quite often with numeric methods. The symbolics would refuse to evaluate that expression (with an inappropriate error messoge, though).
But why would you use lsolve on a system of equations which clearly has no solution (different rank for coefficient matrix and augmented matrix)?
Again you would see numeric inaccuracy if you evaluate the determinant numerically.
BTW, you could install the 30 day eval of Mathcad 15 on a spare computer, if you have that oportunity or in a VM, or use Mathcad Prime2 Express parallel with your MC14. Express won't let you do symbolic operation and solve blocks after its 30 day trial period. Numeric evals should work.