Gaussian Elim: 3x + y - z = -5, -4x + y = 6, 6x -2y + 3z = 2

[tomangseth]

Here is the question I don't understand:

4. Solve the following linear system using Gaussian elimination.

3x + y – z = -5
-4x + y = 6
6x – 2y + 3z = 2

I have tried to solve this. I got 9 1/3 for the answer z. I divided each row by the number in the first row first column. Then I subtracted Row3 from Row 1 and was left with 14/3z=2. Am I on the right track. I asked for an extension on this project and this is the only question that I don't understand. Is the answer 9 1/3 and if so how do I find the answer for x and y? Please help!!

Thanks,

Tomangseth

 

[tkhunny]

Re: Gaussian Elimination

3x + y – z = -5

-4x + y = 6

6x – 2y + 3z = 2

I divided each row by the number in the first row first column.

Why would you do that? Try to make your life easier.

1) 3x + y – z = -5
2) -4x + y = 6
3) 6x – 2y + 3z = 2

-2 x 1) -6x - 2y + 2z = 10
3) 6x – 2y + 3z = 2
Add -4y + 5z = 12
Or 4y - 5z = -12 <== Keep

1) 3x + y – z = -5
2) -4x + y = 6
Add -x + 2y - z = 1
Or x - 2y + z = -1 <== Keep

Recap
1) x - 2y + z = -1
2) -4x + y = 6
3) 4y - 5z = -12

4 x 1) 4x - 8y + 4z = -4
2) -4x + y = 6
Add -7y + 4z = 2
Or 7y - 4z = -2 <== Keep

Recap
1) x - 2y + z = -1
2) 7y - 4z = -2
3) 4y - 5z = -12

-2 x 3) -8y + 10z = 24
2) 7y - 4z = -2
Add -y + 6z = 22
Or y - 6z = -22 <== Keep

Recap
1) x - 2y + z = -1
2) y - 6z = -22
3) 4y - 5z = -12

That's enough of that.

I'm trying to follow my empirical rule - Don't get any intermediate values that are any worse than the ones with which you started - unless absolutely necessary. I'm also following the other important rule - Don't be afraid to write EVERYTHING. Let the notation help you keep track.

 

[tomangseth]

Re: Gaussian Elimination

I kind of see how you did that but I don't understand why you switched the signs after each calculation. Also , for Gaussian elimination I need to solve for x, y, and z.

 

[tomangseth]

Re: Gaussian Elimination

Ok so I just went through all of that and I understand it now. It looks easy the way you did it. The only question I have is why were the signs changed? Thanks alot you did a good job showing me how you arrived at those equations.

 

[tkhunny]

Re: Gaussian Elimination

The only question I have is why were the signs changed? Thanks alot you did a good job showing me how you arrived at those equations.

Housekeeping!

One day I decided that leading negative signs were too often misplaced. The solution is to get rid of them properly before I lose them.

Develop a style that makes sense to you, is useful to you, and is sufficient to the task. If you keep making the same error, change your process.