Let A = (ai,j be an n × n matrix and x = (x1, x2,…, xn), y = (y1, y2,…, yn) be n-vectors, all with real number entries satisfying
If det(A) ≠ 0, then for every y, the linear system of Equations (3.20) has a unique solution x,
Gaussian elimination is a process in which transformations are applied to an invertible matrix A to produce the identity matrix I and thereby obtain the solution for x in Equation (3.20).
Premultiplication of A by Rr, s(v) replaces the rth row of A by the sum of
The inverse of Rr, s(v) is Rr, s(− v).