A new method for determining stoichiometric coefficients using minors of a matrix

The motivation of this study was the investigation into the metallothermic reduction of chromite ores. Spinel materials have complex structures and as a result, balancing of the reduction reactions by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then a new optimised method is proposed. The mathematical basis of both methods is explored using matrix algebra and then demonstrated using a typical chromite reduction reaction.