Why is another row operation necessary to obtain the matrix on the second line?

[mathmathmad]

Homework Statement

[PLAIN]http://img260.imageshack.us/img260/727/picture2mg.png

just wondering.. isn't the the matrix on the 1st line already in its reduced row echelon form?
why is another row operation required to obtain the matrix on the 2nd line? (notice the changes to the matrix on the right)

Homework Equations

The Attempt at a Solution

 

[Mark44]

I don't know what you're trying to do in this problem, but I'll answer your questions. The 3x3 matrix at the right in the top line is NOT in reduced row-echelon form. The matrix at the right in the bottom line is almost in row-echelon form (but not reduced row-echelon form). To get it in row-echelon form, swap the first two rows, then swap the 2nd and 3rd rows.

I think these are the definitions.
Row-echelon form: for each row with a non-zero leading entry, every other row below it has a 0 in that position.
Reduced row-echelon form: same as above, but also every other row above it has a 0 in that position.

Also, you could have done what you did in one step: Add 1 times the 3rd row to the first row.