Thread: Gaussian Elimination, Am I correct?

1. Gaussian Elimination, Am I correct?

I found this (solved) problem in my textbook:
2x + y - 3z = 1
5x + 2y - 6z = 5
3x + y + 4z= 7
This is a 3x3 system. I tried to solve it (using Gaussian elimination algorithm) and got this solution:
z=0.8 y=-2.6 x=3

But, the textbook said that the solution is:
z=1 y=-2 x=3

Which is correct? Me or the textbook?

Thanks.

2. Originally Posted by BanderHM
I found this (solved) problem in my textbook:
2x + y - 3z = 1
5x + 2y - 6z = 5
3x + y + 4z= 7
This is a 3x3 system. I tried to solve it (using Gaussian elimination algorithm) and got this solution:
z=0.8 y=-2.6 x=3

But, the textbook said that the solution is:
z=1 y=-2 x=3

Which is correct? Me or the textbook?

Thanks.
Try this: substitute your solution back into the first of the
equations and evaluate the LHS. Does this equal the RHS?

The answer to this last question is no, try it with the answer
from the text book. Now the RHS and LHS agree.

So what do we conclude?

2. The text book could well be right.

To confirm that the textbook is right substitute its solution
into the other two equations and see if they hold.

RonL

3. I get that you are both incorrect. I used matrices to solve the system and got that:

x = 3
y = $-\frac{26}{7}$
z = $\frac{3}{7}$

I also confirmed by plugging in the books answers into the system that it is incorrect and you can check your own answer by the same method.

4. Originally Posted by Jameson
I get that you are both incorrect. I used matrices to solve the system and got that:

x = 3
y = $-\frac{26}{7}$
z = $\frac{3}{7}$

I also confirmed by plugging in the books answers into the system that it is incorrect and you can check your own answer by the same method.
A more likey explanation is that there has been a transcription error (either
in composing the original question or in editing the textbook )and the last
equation should be:

$
3x-y-4z=7
$

RonL