# gauss jordan help

• Mar 30th 2009, 11:22 AM
wonderstrike
gauss jordan help
Ok here I am working on this problem for like 3 hours to no avail.

x1 + x2 = 1

-x1 + x2 + x3 = -1

-1x2 + x3 = 3

I am trying to solve this in matrix form and get the point of multiplaying a cooefficiant but applying it to this set is baffling my mind. Any insights?

is the matrix

1 1 0
-1 1 0
0 -1 1
• Mar 30th 2009, 12:43 PM
Opalg
Quote:

Originally Posted by wonderstrike
Ok here I am working on this problem for like 3 hours to no avail.

x1 + x2 = 1

-x1 + x2 + x3 = -1

-1x2 + x3 = 3

I am trying to solve this in matrix form and get the point of multiplying a coefficient but applying it to this set is baffling my mind. Any insights?

is the matrix

1 1 0
-1 1 0
0 -1 1

You should use an "augmented" matrix, with an extra column consisting of the coefficients on the right=hand side of the equations. So the matrix is $\begin{bmatrix}1&1&0&1\\ -1&1&1&-1\\ 0&-1&1&3\end{bmatrix}$. Now apply the Gauss–Jordan process to the matrix, and then you should be able to read off the solution.
• Mar 30th 2009, 02:05 PM
wonderstrike
$

\begin{bmatrix}1&1&0&1\\ 0&1&.5&0\\ 0&0&1&2\end{bmatrix}

$

$
\begin{bmatrix}1&0&0&2\\ 0&1&0&-1\\ 0&0&1&2\end{bmatrix}$

have I broken this down right? so the answer would be the last column 2,-1,2

?
• Mar 30th 2009, 11:28 PM
Opalg
Quote:

Originally Posted by wonderstrike
$

\begin{bmatrix}1&1&0&1\\ 0&1&.5&0\\ 0&0&1&2\end{bmatrix}

$

$
\begin{bmatrix}1&0&0&2\\ 0&1&0&-1\\ 0&0&1&2\end{bmatrix}$

have I broken this down right? so the answer would be the last column 2,-1,2

?

That is correct (as you could check for yourself by substituting 2, –1, 2 for $x_1,x_2,x_3$ in the original equations).