Let us suppose we are given a set of linear equations to solve. Here represents a square matrix of nth order and and vectors of th order. We may either treat this problem as it stands and attempt to find , or we may solve the more general problem of finding the inverse of the matrix , and then allow it to operate on giving the required solution or the equation as . If we are quite certain that we only require the solution to be the one set of equations, the former approach has the advantage of involving less work (about one-third the number of multiplications by almost all methods). If, however, we wish to solve a number of sets of equations with the same matrix it is more convenient to work out the inverse and apply it to each of the vectors . This involves, in addition, multiplications and recordings for each vector, compared with a total of about multiplications in an independent solution.
— Alan Turing (1948)