Finding reduced row echelon form of a 3×3 matrix

[ThomasHW]

Homework Statement

Find the reduced row echelon form of the following matrix:

$$\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;-4 & 0 & 4\;\\\;2 & -4 & 1\\\;-4 & 4 & -2\end{vmatrix}$$

The Attempt at a Solution

$$\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;1 & 0 & 1\;\\\;0 & 1 & \frac{1}{4}\\\;0 & 0 & 1\end{vmatrix}$$

I've tried it a few times and keep getting that answer. I've inputted that answer and it's wrong. Am I supposed to keep reducing the third row (even though those are constants?)

 

[dontdisturbmycircles]

Look at your last row. It says 0x+0y=1 (Assuming this is an augmented matrix)

 

[ThomasHW]

I figured it out. I was supposed to make the 1 and 1/4 in the third row zero's as well.

 

[HallsofIvy]

Yes, what you showed was "row echelon" form. "Reduced row echelon reduces above the diagonal also. Actually, until you get down to a row all 0s you will have just the identity matrix.

 

[ThomasHW]

I had assumed not to touch the last row because that is usually the row of constants. In this case it wasn't - I had just assumed it was.