If we reduce A to reduced
echelon form, the *leading entries* are in
the **pivot
positions** of A.

It turns out that we can locate the pivot positions
by reducing A to
echelon form only. The entries in these
positions are
called **pivots**, while the columns they appear in are called
**pivot
columns**.

For example, the matrix

3 | -7 | 8 | -5 | 8 | 9 |

3 | -9 | 12 | -9 | 6 | 15 |

0 | 3 | -6 | 6 | 4 | 5 |

is row equivalent to

3 | -9 | 12 | -9 | 0 | -9 |

0 | 2 | -4 | 4 | 0 | -14 |

0 | 0 | 0 | 0 | 1 | 4 |

and so we know that the pivot positions are those containing red numbers. Also, the first, second and fifth columns are pivot columns.