# This linear system has a solution? (Gauss' elimination)

• I

## Summary:

I have the following linear equation
-3x1 +x2-2x3 =-7
5x1 + 3x2-4x3 = 2
x1 + 2x2-3x3 = -1

And I wonder it has a solution, because I found the third line as:
0 0 0 = -49/6

## Main Question or Discussion Point

I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws. Related Linear and Abstract Algebra News on Phys.org
mathwonk
Homework Helper
I didn't check your work, but I urge you to do it again. I taught this for years and always made mistakes on every calculation unless I did every step in complete detail. no shortcuts at all.

I didn't check your work, but I urge you to do it again. I taught this for years and always made mistakes on every calculation unless I did every step in complete detail. no shortcuts at all.
I think that the calculations shown in photo is enough to someone who already know a little solving linear systems.
but I urge you to do it again.
Here you refer to solve again the question?

mathwonk
Homework Helper
"I think that the calculations shown in photo is enough to someone who already know a little solving linear systems."

I think you are missing the point, i don't have a problem, you do.

"I think that the calculations shown in photo is enough to someone who already know a little solving linear systems."

I think you are missing the point, i don't have a problem, you do.
Sir, what kind of problem are you speaking of? I don't get it what I actually should do ?

mathwonk
Homework Helper
Forgive me, I am only suggesting if you are in doubt as to whether a gaussian elimination is correct, you should do it again, and see if you get the same answer.

Forgive me, I am only suggesting if you are in doubt as to whether a gaussian elimination is correct, you should do it again, and see if you get the same answer.
I get it but I had wondered this case which I add below. Isn't it time wasting making an effort to solve whole question again mathwonk
Homework Helper
"Isn't it time wasting making an effort"? indeed whose time do you speak of?

"Isn't it time wasting making an effort"? indeed whose time do you speak of?
Man it's 4 am here :D I'm doing a homework for 5 hours. So my time...

Man it's 4 am here :D I'm doing a homework for 5 hours. So my time...
I don't want to be misunderstood, I am wasting my time, not you.

mathwonk
Homework Helper
pardon me for being flippant. i share your experience at trying to get gaussian calculations correct as i said. but the sad truth is there is no other way but to do them over and over until all errors are eliminated. and if you are up that late doing hw, perhaps you could learn to do it earlier next time?

• requied
if you are up that late doing hw, perhaps you could learn to do it earlier next time?
You are right at this point, thanks to you for all motivations. All the best :)

mathman
Calculate the determinant (I get 0). There is no solution! That's the problem!

• Delta2 and requied
There is no solution!
So the actual answer is this, right?

WWGD
Gold Member
2019 Award
Why dont you compute the determinant of the original matrix to see if it is 0 too? Not a guarantee if it is, but shows a problem if it is not. The determinant of the original matrix is 0. I don't know what happens if a determinant of a matrix is 0.

WWGD
Gold Member
2019 Award
View attachment 263424
The determinant of the original matrix is 0. I don't know what happens if a determinant of a matrix is 0.
One of the consequences is that there is a vector b for which Ax=b has no solution. And the matrix is not invertible.

mathman
The determinant is 0 means that the equations are not linearly independent, so you can't get a solution. Getting (0,0,0) for the left side after Gauss elimination is equivalent to a 0 determinant.

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