chemical reaction balancing online

• the Maple assignment reaction [pdf, mw] (an explosive  lead azide PbN₆ with reaction product chromium permanganate CrMa₂N₈) is found balanced here: http://www.webqc.org/balancedchemicalequations-081002-18.html
  which also has bazillions of other reactions listed for mental games... at the chem site reaction balancer
• googling the previous two chemicals shows that this equation is occasionally used in linear algebra courses.
• the additional exercise is solved in this version of the worksheet: mw