A **subtlety **in property #1 in identifying a ref or rref matrix

My linear algebra book says for property #1 as follows:

1) If a row does not consist entirely of zeros, then the first nonzero number in the row is a 1. We call this a leading 1.

Then I came up with my own matrix in my mind and started questioning property #1.

2 1 5 1

0 0 1 0

Would the number 2 in the first row of this matrix be the "leading 1" ...after all the textbook did say "first nonzero number"?

**Edited by warnexus, 22 February 2014 - 09:32 PM.**