title: Solving a system of linear equations in a non-square matrix
body: <p>I have a system of linear equations that make up an <strong><code>NxM</code></strong> matrix (i.e. Non-square) which I need to solve - or at least <em>attempt</em> to solve in order to show that there is no solution to the system. (more likely than not, there will be no solution)</p>
  
  <p>As I understand it, if my matrix is not square (over or under-determined), then no <strong>exact solution</strong> can be found - am I correct in thinking this? Is there a way to transform my matrix into a square matrix in order to calculate the determinate, apply Gaussian Elimination, Cramer's rule, etc?</p>
  
  <p>It may be worth mentioning that the coefficients of my unknowns <em>may</em> be zero, so in certain, rare cases it would be possible to have a zero-column or zero-row.</p>