Systems of linear equations

Abstract

In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important rolls. A system of linear equations has the form

$$ {a_{11}}{x_1} + {a_{12}}{x_2} + \cdots + {a_{1n}}{x_n} = {b_1}{\text{ }}{a_{21}}{x_1} + {a_{22}}{x_2} + \cdots + {a_{2n}}{x_n} = {b_2}{\text{ }} \vdots {\text{ }}{a_{m1}}{x_1} + {a_{m2}}{x_2} + \cdots + {a_{mn}}{x_n} = {b_n}.{\text{ }} $$

(L)