  I propose a novel approach to balancing equations that is applicable to all
chemical-reaction equations; it is readily accessible to students via
scientific calculators and basic computer spreadsheets that have a
matrix-inversion application. The new approach utilizes the familiar
matrix-inversion operation in an unfamiliar and innovative way; its purpose is
not to identify undetermined coefficients as usual, but, instead, to compute a
matrix null space (or matrix kernel). The null space then provides the
coefficients that balance the equation. Indeed, the null space contains
everything there is to know about balancing any chemical-reaction equation!
