what is linear algebra Solution Linear Algebra is a branch of mathematics as old as mathematics itself. The solving of the simple linear equation ax + b = 0 may be considered as the original problem of this subject. Although this problem presents absolutely no difficulty at all, the method which solves it (i.e. if a â€š 0, then the unique solution is given by x = (-b)/a, no solution if a=0 and b â€š 0 and infinitely many solutions if both a and b are zero), together with the properties of the corresponding linear function y=ax+b, are fundamental models for the ideas and methods of all of linear algebra. .