My decision to add to the mountainous pile of verbage that has accumulated over the years on the subject of balancing chemical-reaction equations surprised even me.  The world has long known, of course, that matrix null space vectors are the comprehensive solution to balancing these often-irksome equations.  Getting to those vectors, however, required specialized computer algorithms or long, long hours with a pencil.  But I had a small epiphany one day and realized that one could use the common, widely-available, matrix inverse function to calculate null-space vectors!  And that meant, obviously, that anyone with a scientific calculator or a standard spreadsheet program on his computer could calculate null-space vectors and balance any chemical-reaction equation quickly and accurately.

 My paper on this technique was published originally in “The Chemical Educator.”  It is now available, open access, at:  http://arxiv.org/abs/1110.4321  (See the PDF file in the Download section there for a complete explanation and full documentation.)