Roughly speaking, this method: http://www.wikihow.com/Balance-Chemical-Equations

Showing work is required, and if work contains a matrix then they'd just mark it as zero.

> Showing work is required, and if work contains a matrix then they'd just mark it as zero.

Ugh, this makes me so angry and resentful ...

School's first objective is to make you obey.

Looks isomorphic to what you can do with matrices (including some heuristics to what rows to go for first). Of course, that doesn't make it better.

by placing backdoors in his technique.