Proposed method to reduce the determinant of order n

TL;DR

This paper introduces a theorem for reducing the order of determinants through transformations into second-order determinants, aiming to simplify calculations and improve educational approaches.

Contribution

It proposes a novel theorem that transforms determinants into smaller ones, enhancing computational efficiency and pedagogical simplicity compared to traditional methods.

Findings

The method effectively reduces determinant order to second order.

It shows improved efficiency over minors and Gauss methods.

The approach is easy to understand and apply in teaching contexts.

Abstract

This paper presents a theorem which solves the problem of reduction of the determinant order by means of a transformation of it, into other determinant whose each element are a determinant of second order. This implies that, if the process continues, desired result is obtained by solving always determinants of second order. It also assesses the degree of efficiency compared to the method by minors and with the method of Gauss, as well as the ability to reflect small variations in the data. This method should have a good impact also in the area of teaching mathematics, due to its ease of assimilation and application.