# Cramer-type Formula for the Polynomial Solutions of Coupled Linear Equations with Polynomial Coefficients

### Tateaki Sasaki

University of Tsukuba, Ibaraki, Japan

## Abstract

This paper derives a determinant form formula for the general solution of coupled linear equations with coefficients in *K*[_x_1,…⋯, *xn*], where *K* is a field of numbers, the number of unknowns is greater than the number of equations, and the solutions are in *K*(_x_1,…⋯, *xn*–1)[*xn*]. The formula represents the general solution by the minimum number of generators, and it is a generalization of Cramer's formula for the solutions in *K*(_x_1,…⋯, *xn*). Compared with another formula which is obtained by a method typical in algebra, the generators in our formula are represented by determinants of quite small orders.

## Cite this article

Tateaki Sasaki, Cramer-type Formula for the Polynomial Solutions of Coupled Linear Equations with Polynomial Coefficients. Publ. Res. Inst. Math. Sci. 21 (1985), no. 1, pp. 237–254

DOI 10.2977/PRIMS/1195179845