Exercise 1 Page 499

Let's first take a look at an example of a stair-step pattern in a system of equations. x+3y-4z=17 & (I) y+7z=5 & (II) z=8 & (III) Note that in each equation, the coefficient of the first variable — called the leading coefficient — is 1. 1* x+3y-4z=17 & (I) 1* y+7z=5 & (II) 1* z=8 & (III) Looking at these equations, you can see they line up like a staircase, each one simpler than the one above. This pattern is known as row-echelon form. The term echelon actually comes from French, where it means a step or level. Now we can finish the definition.