Reduced Row Echelon Form

[Clydey]

Hey all. I'm trying to get my head around RREF. I feel like I'm sometimes doing operations in the wrong order. I'll give you an example.

1 3 -3 -3
0 0 -2 2

From this, I ended up with:

1 3 0 -12
0 0 1 -1

The correct answer (from a calculator) is:

1 3 0 -6
0 0 1 -1

Now, I understand how to arrive at the correct answer. You divide the 2nd row by -2 and then do the relevant calculation on the two rows after. I did the calculation first and then divided the 2nd row by -2 to arrive at my answer.

Based on the tutorials I've watched, none of the tutors have insisted that you must turn the pivot into a 1 before doing other row operations. In fact, one said to concentrate on zeroing out first because the 1s are easier to get. So what am I missing? My ability to get the correct answer is inconsistent at this point, as it seems to depend on whether I, by some good fortune, do everything in the correct order.

Any help is greatly appreciated.

 

[Dr.Peterson]

Write out the actual calculations you did for the first row, and I think you'll see the error.

Presumably you added -3/2 times row 2 to row 1. If you do that consistently, you will get the correct answer.

What did you really do to get -12?

(Dividing the second row by -2 first is just a way to make the work easier by avoiding fractions; it isn't necessary.)

 

[Clydey]

I did: R1 = 2xR1 + (-3R2).

So -6+(-6) = -12

Am I missing something obvious?

 

[Dr.Peterson]

That's not what you did to the first two columns! I mentioned "doing it consistently" for a reason.

If you want to leave any entries unchanged, you don't want to multiply that row. Commonly, we always do something like R1 + n*R2, not m*R1 + n*R2 (though there are different styles). But if you do the latter, be consistent, and then go back later and divide rows as needed. Don't just leave entries unchanged because you want to.

 

[Clydey]

That's not what you did to the first two columns! I mentioned "doing it consistently" for a reason.

If you want to leave any entries unchanged, you don't want to multiply that row. Commonly, we always do something like R1 + n*R2, not m*R1 + n*R2 (though there are different styles). But if you do the latter, be consistent, and then go back later and divide rows as needed. Don't just leave entries unchanged because you want to.

Oh, I see what you're saying. The way I did it, I should have ended up with this in the first row:

2 6 0 -12

Whoops. Thanks for helping me out.