Please HELP!
I have a problem to solve with the Gauss metohd.
{ X1 + X2 + 3X3 + 2X4 + 2X5 = 3
{ X1 + X2 + X3 + 2X4 = 1
{ X1 + X2 - X3 + 2X4 - 2X5 = -1
{ -X1 + X2 + X3 = 1
Thanks!
You are THE BEST
The augmented matrix is:
$\displaystyle
\left[
\begin{array}{ccccc}
1&1&3&2&3\\
1&1&1&2&1\\
1&1&-1&2&-1\\
-1&1&1&0&1
\end{array}
\right]
$
Now subtract the first row from the second and third rows and add it to the third row to get:
$\displaystyle
\left[
\begin{array}{ccccc}
1&1&3&2&3\\
0&0&-2&0&-2\\
0&0&-4&0&-4\\
0&2&4&2&4
\end{array}
\right]
$
Now interchange the last row with the second row:
$\displaystyle
\left[
\begin{array}{ccccc}
1&1&3&2&3\\
0&2&4&2&4\\
0&0&-4&0&-4\\
0&0&-2&0&-2
\end{array}
\right]
$
Now because the last two rows are identical it means that one of the variables will be indeterminate, and we might as well let this be $\displaystyle x_4$. We also observe that the last two rows mean that $\displaystyle x_3=1$.
Now substituting into the equation corresponding to our second row:
$\displaystyle 2x_2+4+2x_4=4$
so:
$\displaystyle
x_2=-x_4
$
Now substituting into the equation corresponding to our first row:
$\displaystyle x_1-x_4+3+2x_4=3$
so:
$\displaystyle
x_1=-x_4
$
CB