Light Off Problem

Abstract

Linear Algebra presents a very important role in the areas of accuracy, and through it we can show its utility in modeling a problem that involves a simple game of erasing and lighting lights, after modeling the problem, we will solve it by implementing an algorithm of elimination of Gauss in Scilab (Scilab is free and open source software, focused on numerical computation similar to Matlab). The game, Lights Out, is a famous game of the 90's, which consists of 25 keys illuminated and arranged in the form of a 5x5 matrix, where it has an initial state and we must delete all keys by pressing a correct sequence of keys, this sequence will be provided by the program implemented in Scilab, ie we will have an immediate solution to erase all lights in the game. The modeling uses Linear Algebra concepts: matrices, determinants and linear systems, together with the concept of the set of the rest of the division by 2().