# Linear Algebra: Can I do this for Reduced Echelon Form?

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## 3 Replies - 264 Views - Last Post: 04 March 2014 - 09:02 PM

### #1 streek405

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# Linear Algebra: Can I do this for Reduced Echelon Form?

Posted 24 February 2014 - 12:54 AM

I've been working on my hw for an hour now and just took a glance at my notes and think that I have been solving matrices incorrectly. The reason I say this is because my notes say that there are 5 steps to get to reduced echelon form:
For matrix
A B C
D E F
G H I

1. Get A to be 1
2. Get D and G to be 0
3. Get E to be 1
4. Get H to be 0
5. Get I to be 1

My end result is in echelon form but I am wondering if my answer is still correct if I do not follow the steps in order.
For example, if I solve it by doing it in the following order, and my answer still looks like echelon form, is my answer still correct?

How I have been doing it:
1. Get A to be 1
2. Get D to be 0
3. Get E to be 1
4. Get G and then H to be 0
5. Get I to be 1

Also, am I allowed to multiply the entire last row by zero, if the previous rows are in echelon form?

For example, if I have this near the end:
1 -2  2 11
0  0  1  2
-2 4  0 -14

can I just turn it into this by doing R3 ---> 0*R3
1 -2  2 11
0  0  1  2
0  0  0  0

?

This post has been edited by macosxnerd101: 24 February 2014 - 07:42 AM
Reason for edit:: Added code tags around matrices for formatting

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## Replies To: Linear Algebra: Can I do this for Reduced Echelon Form?

### #2 macosxnerd101

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## Re: Linear Algebra: Can I do this for Reduced Echelon Form?

Posted 24 February 2014 - 07:43 AM

No. R3 <-- 2R1 + R3.

### #3 streek405

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## Re: Linear Algebra: Can I do this for Reduced Echelon Form?

Posted 24 February 2014 - 10:03 PM

macosxnerd101, on 24 February 2014 - 07:43 AM, said:

No. R3 <-- 2R1 + R3.

Ok thanks. Can I solve the matrix in any order that I want to, like how I stated above?

### #4 Gatmah

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## Re: Linear Algebra: Can I do this for Reduced Echelon Form?

Posted 04 March 2014 - 09:02 PM

You can solve the matrix in any order you want as long as you know what you're doing. You really can't multiply by zero because you would end up with coefficients that can be divided by zero to return to their original values.