On the genesis of a determinantal identity

TL;DR

This paper derives a specific 3x3 determinantal identity involving 12 variables, providing an explicit formulation related to completing unimodular rows, building on prior theoretical results.

Contribution

It introduces a new explicit determinantal identity that advances understanding of unimodular row completion in algebraic K-theory.

Findings

Derived a 3x3 determinantal identity with 12 indeterminates

Connected the identity to existing results on unimodular rows

Provided explicit formulas enhancing algebraic methods

Abstract

We show how to derive a $3 \times 3$ determinantal identity in 12 indeterminates that gives an explicit version of a result of Mohan Kumar and Pavaman Murthy on completing unimodular rows.