# Thread: gaussian elimination - urgent help

1. ## gaussian elimination - urgent help

hi,

im trying to solve a set of equations by guassian elimination,

i got it this far

1 0 -1 2 0
0 1 2 3 0
0 0 0 0 1

sorry havent figured out how to use the maths tags yet.
should i have

X1 -X3 +2X4 = 0
X2 + 2X3 + 3X4 = 0

2. umm, what are the equations?

3. Originally Posted by jonbob81
hi,

im trying to solve a set of equations by guassian elimination,

i got it this far

1 0 -1 2 0
0 1 2 3 0
0 0 0 0 1

sorry havent figured out how to use the maths tags yet.
should i have

X1 -X3 +2X4 = 0
X2 + 2X3 + 3X4 = 0

wouldn't the last row imply that there are no solutions ?

Bobak

4. Does the matrix equal anything? (is it a matrix?)

If it does then we might be able to go somewhere since we'll have the value of one of the unknowns.

I'm really just speculating since i'm a tad confused.

5. The last row of the matrix implies that $\displaystyle 0\cdot x_1+0\cdot x_2 +0\cdot x_3 + 0\cdot x_4=1 \Leftrightarrow 0=1$ which is false. Thus the set of equations has no solution.

6. hi its the following set of equations

2x1 − x2 + x4 = −1
−x1 + x2 + 2x3 + x4 = 5
x1 + 2x3 + 2x4 = 4

7. hmm, this is looking a bit peculiar. I did a little something that went like this:

The equations we have are:

$\displaystyle 2x_{1}-x_{2}+x_{4}=-1$------>equation 1)
$\displaystyle -x_{1}+x_{2}+2x_{3}+x_{4}=5$----->equation 2)
$\displaystyle x_{1}+2x_{3}+2x_{4}=4$----->equation 3)

2)-3)= $\displaystyle -2x_{1}-x_{2}-x_{4}=1$
but 10 is $\displaystyle 2x_{1}-x_{2}+x_{4}=-1$.
This implies that $\displaystyle x_{1}=x_{4}=0$

As a result, the equations now become:
$\displaystyle x_{2}=-1$
$\displaystyle x_{2}+2x_{3}=5$
$\displaystyle 2x_{3}=4$ or $\displaystyle x_{3}=2$

However, the values of $\displaystyle x_{2}$ and $\displaystyle x_{3}$ now conflict with equation two.

I don't think these equations have solutions....