2015-3: Farey Tale

In mathematics, the Farey_sequence of order n is the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size. Each Farey sequence starts with the value 0, denoted by the fraction 0⁄1, and ends with the value 1, denoted by the fraction 1⁄1.

Write code that takes an integer argument and returns a 2x2 matrix of the terms in the Farey sequence of that order. Each element in the returned vector is itself a 2-element vector of numerator and denominator for the corresponding term.