# Augmented Matricies

• Mar 21st 2014, 05:53 PM
sakonpure6
Augmented Matricies
Did I approach this problem correctly? Am I able in the last matrix drawn to do: R3 - R2 for the second row and then R2-R3 for the third row? Also, does it imply that I am using the vectors from the matrix above for R2 and R3?
Attachment 30482
• Mar 21st 2014, 08:12 PM
romsek
Re: Augmented Matricies
What you did wasn't correct. Look at the attached pic.

Attachment 30483
• Mar 22nd 2014, 06:18 AM
sakonpure6
Re: Augmented Matricies
where did I do wrong in my approach, I do not understand!
• Mar 22nd 2014, 06:37 AM
romsek
Re: Augmented Matricies
Quote:

Originally Posted by sakonpure6
where did I do wrong in my approach, I do not understand!

once you replace a row via one of the row operations you cannot go back and use the old row.
• Mar 22nd 2014, 08:13 AM
sakonpure6
Re: Augmented Matricies
I still am not getting the right answer, what did I do wrong now ? (Edit: Ignore my x,y,z solution I messed it up, but please look at my matrix)
Attachment 30487

Thank you
• Mar 22nd 2014, 08:31 AM
romsek
Re: Augmented Matricies
Quote:

Originally Posted by sakonpure6
I still am not getting the right answer, what did I do wrong now ? (Edit: Ignore my x,y,z solution I messed it up, but please look at my matrix)
Attachment 30487

Thank you

You're not even remotely doing it right. You want to end up with 0's below the diagonal. I suggest you go back to the book and look at some examples.
• Mar 22nd 2014, 09:40 AM
sakonpure6
Re: Augmented Matricies
I have another question: Let's say we have

R1, R2, R3 (representing scalar equations on a plane) and we perform for example
R2 = R3-R1
So, we now have R1,R2',R3

Can we then do this: R3=R2' - 3R1 ? or we can not use R2' ever again?
• Mar 22nd 2014, 02:44 PM
romsek
Re: Augmented Matricies
Quote:

Originally Posted by sakonpure6
I have another question: Let's say we have

R1, R2, R3 (representing scalar equations on a plane) and we perform for example
R2 = R3-R1
So, we now have R1,R2',R3

Can we then do this: R3=R2' - 3R1 ? or we can not use R2' ever again?

I believe you mean R2' = R3 - R1.

You can use R2' after this. What you can't use is R2.

I shouldn't say can't. R2 is still a valid equation and as such you can add multiples of it to the other equations. But if you are doing things correctly you shouldn't want to.

Generally at the kth step you want to use the normalized kth row, which now has 0's in columns 1, k-1, and a 1 at column k, to zero out the k+1, nth rows.

So you normalize row 1, zero out column 1 in rows 2 and 3.

Then normalize row 2. Zero out the 2nd column in row 3.

Normalize row 3 and you are in upper triangular form and can back substitute.

This works fine however what you might also do, to avoid the fractions getting too obnoxious from normalization, is swap rows. Especially if a row already has a 1 in the column you are about to zero out. In that case you don't need to normalize it.

Do you have to normalize during each step? No. You can leave normalization to the end and add or subtract multiples of your "pivot row" (the row that's being used to zero out the others) to a multiple of the row being zeroed and there are actually good reasons numerically to do this. But if your row is all multiples of the pivot element then by all means normalize it.

Your best bet to learn this is to write up a small program to toss 3x3 or 4x4 matrices at you to row reduce and solve. Then check the answers but plugging the solutions back in. Keep at this until you start to get every one correct.

This diatribe probably leaves you more confused than you were. Maybe look at this.
• Mar 22nd 2014, 04:34 PM
sakonpure6
Re: Augmented Matricies
Thank you for that resource it is very helpful!

Edit: As part of my Independent study, I do not see how Matrixes are any useful or better than solving the intersection of planes or lines in 3D or 2D. So why bother with Matrix? Is there any long term benefit?
• Mar 22nd 2014, 06:11 PM
sakonpure6
Re: Augmented Matricies
Since I couldn't edit my previous post:

If my 3rd row in my matrix is for example [0 0 18 | 36] do I have to draw another Matrix and show the simplification [0 0 1 | 2] or can I just algebraically? Is it considered a communication error If I do not show the simplification in a matrix format?

and Is my format correct here, Also can I simply the equations before starting solving my augmented matrix like I did here:
Attachment 30493