AbstractThe advent of the electronic computer has brought the problem of the solution of simultaneous linear equations to the fore, particularly in regard to the solution of symmetrical equations such as normal equations in least squares solutions. The object of this paper will be to remind readers of some of the usual ways of solving simultaneous equations, and then to discuss in greater detail the solution of normal equations by the Gauss–Doolittle, Cholesky and other methods with modifications and explanations.