Matrix Representation of Linear Equations

A set of linear equations can be represented in matrix form. Ex:

can be written in the matrix form as

or concisely

[a][x] = [b]

[a] is called the coefficients matrix.
[b] is called the Right Hand Side (RHS) vector.
[x] is called the solution vector.

The row index in the coefficients matrix and the index in the RHS vector represent the index of the equation.
The column index in the coefficients matrix and the index in the solution vector represent the index of the unknown.