TITLE: What does echelon mean?
QUESTION [7 upvotes]: When you solve a system of linear equations, you write down the augmented matrix and reduce this to reduced row echelon form. What is the meaning of the word echelon?

REPLY [5 votes]: From Online Etymology Dictionary:

echelon (n.)
1796, echellon, "step-like arrangement of troops," from French échelon "level, echelon," literally "rung of a ladder," from Old French eschelon, from eschiele "ladder," from Late Latin scala "stair, slope," from Latin scalae (plural) "ladder, steps," from PIE $\ast$skand- "to spring, leap" (see scan (v.)). Sense of "level, subdivision" is from World War I.

Steven Schwartzman's The Words of Mathematics: An Etymological Dictionary of Mathematical Terms (MAA, 1994) also attributes the root of the term to the French word échelon and its meaning of "rung of a ladder" (link from Google Books).
The earliest appearance of "echelon form" as a linear algebra term that I can find is in Birkhoff and Mac Lane (1953), A Survey of Modern Algebra (link from Google Books). Yet, Nathan Jacobson's Lectures in Abstract Algebra: II. Linear Algebra (1953) does not contain this term. I guess the term was introduced to linear algebra more or less around the 1950s.