Gauss-Jordan reduction stuck on system of three equations

[paulchem]

Use Gauss jordan reduction


Hi, sorry for introducing myself. I was just frustrated because I've been trying to do this problem for awhile.

4x+y-3z=11
2x-3y+2z=9
x+y+z=-3



4 1 -3 11
0 -1 0 3
0 3 7 -23

R2+2R3-->R2
4R3+-R1-->R3


3R1+-R3-->R1
4 0 2 56
0 -1 0 3
0 3 7 -23

I'm stuck here.

The calculator gave me

1 0 0 7/18
0 1 0 -3
0 0 1 -7/18

Please tell me where I went wrong thanks

 

[Hurkyl]

One thing I often do with these type of problems is that I redo the work from scratch -- I usually won't make the same mistake both times. (swapping rows around decreases the odds of remaking the mistake too)


That being said, you made an arithmetic error computing R2+2R3-->R2.

 

[Benny]

I think a good idea when you start one of these questions is to first eliminate any coefficients of x which are greater than 1. So in the case of your question, starting with the given system, I would do:

R1' = R1 - 4R3
R2' = R2 - 2R3

 

[saltydog]

Hello PaulChem. You know, I'm not trying to be critical, really I'm not, but those numbers look a little "busy", hard to follow. I don't expect you to know now how to make some really nice math format using LaTex which you can learn all about by jumping to the Physics Forum and checking out "Introducing LaTex". But here is what it would look like with a little formatting. Just double click on it and a small window will pop up showing the LaTex commands:

$$\left[ <br /> \begin{array}{cccc}<br /> 4 & 1 & -3 & 11 \\<br /> 0 & -1 & 0 & 3 \\<br /> 0 & 3 & 7 & -23 <br /> \end{array}<br /> \right]$$

Edit: alright single click, whatever. I get confussed.

 

[Hurkyl]

And if you want to draw a partitioned array...

$$<br /> \left(<br /> <br /> \begin{array}{ccc|c}<br /> <br /> 4 & 1 & -3 & 11 \\<br /> <br /> 0 & -1 & 0 & 3 \\<br /> <br /> 0 & 3 & 7 & -23 <br /> <br /> \end{array}<br /> <br /> \right)<br />$$

 

[saltydog]

And if you want to draw a partitioned array...

$$<br /> \left(<br /> <br /> \begin{array}{ccc|c}<br /> <br /> 4 & 1 & -3 & 11 \\<br /> <br /> 0 & -1 & 0 & 3 \\<br /> <br /> 0 & 3 & 7 & -23 <br /> <br /> \end{array}<br /> <br /> \right)<br />$$

Oh that is so much nicer. Mine is crummy.

Edit: Yep, PaulChem, I say do the whole problem again using Hurkly's format, step by step, nice "partitioned arrays", cut and past his commands into your post. With a final line saying: x, y, and z are: