Matrix calculation

Overview

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AUTHORS

Gérard DEBEAUMARCHÉ: Former student at the École normale supérieure de Cachan - Special mathematics teacher at Lycée Clemenceau, Reims
Danièle LINO: École normale supérieure de Sèvres alumnus - Special mathematics teacher at Lycée Clemenceau, Reims

INTRODUCTION

A large number of mathematical and applied problems involve studying (and solving) systems of linear equations. The system (S) : ${\begin{cases} a_{11} x_{1} + \dots + a_{1 p} x_{p} \\ ⋮ \\ a_{n 1} x_{1} + \dots + a_{np} x_{p} \end{cases} \begin{matrix} = b_{1} \\ ⋮ \\ = b_{n} \end{matrix}$

(where the unknowns are the numbers $x_{1}, \dots, x_{p}$ and where the numbers a _ij and b _i are given in $K$ ) is also noted, in matrix form : $(\begin{matrix} a_{11} & \dots & a_{1 p} \\ ⋮ & ⋮ \\ a_{n 1} & \dots & a_{np} \end{matrix}) (\begin{matrix} x_{1} \\ ⋮ \\ x_{p} \end{matrix}) = (\begin{matrix} b_{1} \\ ⋮ \\ b_{n} \end{matrix})$