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Part of 1. Systems of Linear Equations and Matrices

$\begin{array}{lcl} a_{11}x_1 + a_{12}x_2 + \ldots + a_{1n}x_n = b_1 \ a_{21}x_1 + a_{22}x_2 + \ldots + a_{2n}x_{n} = b_2 \ \vdots \ a_{m1}x_1 + a_{m2}x_2 + \ldots + a_{mn}x_n = b_m \end{array}$

The double subscript on coefficients $a{ij}$ gives their location in the system, with the $_{i}$ indication the equation in which the coefficient appears, and the $_{j}$ indicating the unknown it multiplies.

A solution for a system is the the sequence of numbers that, when substituted for the unknowns ( $x_i$ ), makes each equation a true statement.

Alternatively, they can be seen as matrix coordinates, with the first subscript indicating the row the coefficient is located in, and the second indicating the column the coefficient is located in.

Referenced in

1. Systems of Linear Equations and Matrices

1. Systems of Linear Equations and Matrices