Linear equation

Definition

Let $F$ be a field and let $n \ge 1$ be an integer. A linear equation over $F$ in the unknowns $x_1, \dots, x_n$ is an equation of the form $$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b,$$ where the coefficients $a_1, \dots, a_n$ are elements of $F$. The constant term $b$ is also an element of the field. A solution of the equation is a tuple $(s_1, \dots, s_n) \in F^n$ such that $a_1 s_1 + \cdots + a_n s_n = b$.