A formula for decreasing the order of a Determinant

 

Introduction

 

     We often employ the Laplace Expansion method, which is discuss in most textbooks, to evaluate determinants of higher order. Here is another method to decrease the order of an determinant. Hope you enjoy it.

 

Decreasing order formula

 

 

Multiplying the first column respectively by ,  and then add to the 2nd column, 3rd column, n-th column, we can get:

 

            

     The last determinant is of order (n-1). It is a determinant with each entry an order two determinant. It seems difficult in the first glance. However, if you study it closely there are some pattern in the entries.

 

 

An example