# History of solving linear equations with matrices

I'm solving linear equations with matrices right now and I wonder, how did it start.

Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or linear equation? How did they found each other?

This is information may be incorrect at times, I think I got it from E.T.Bell's Men of Mathematics and an (french) exercice book. Gauss already used 3 by 3 arrays of numbers to describe maps, and I think his student Eisenstein introduced the notation $\frac{1}{S}$ to denote the inverse of $S$, but that notation was later abandoned. – Olivier Bégassat Oct 20 '11 at 0:54