Matrix question

In matrix-form, it looks like this:

[tex]\left( {\begin{array}{*{20}c}
1 & 1 & 1 & 0 & 2 \\
2 & 0 & 2 & 2 & 2 \\
1 & 2 & 2 & 0 & 1 \\
2 & 2 & 0 & 1 & 2 \\
\end{array}} \right)[/tex]

Do you know how Gaussian elimination works?

 

How about this:

[tex]\left(
\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\
2 & 0 & 2 & 2 & 2 \\
1 & 2 & 2 & 0 & 2 \\
2 & 2 & 0 & 1 & 1
\end{array}\right)
[/tex]

That's the augumented matrix Niteshadw.

So, reduce it. Here, I'll do the first part. I'll multiply the top row by -2 and then add it to the second row yielding:

[tex]
\left(
\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2 \\
0 & -2 & 0 & 2 & -2 \\
1 & 2 & 2 & 0 & 2 \\
2 & 2 & 0 & 1 & 1
\end{array}\right)
[/tex]

Can you continue doing this until you get it to row-reduced form?

 

Typo!! The first matrix in Saltydog's response should be
[tex]\left(\begin{array}{cccc|c}1 & 1 & 1 & 0 & 2\\ 2 & 0 & 2 & 2 & 2 \\ 1 & 2 & 2 & 0 & 1 \\ 2 & 2 & 0 & 1 & 2 \end{array}\right)[/tex]

Except for separating out the "augmenting" part, that's just what TD said.

 

I think you row-reduced fine but the last column refers to the constants, not to an unknown. So the solution should be:

[tex]\left\{ \begin{array}{l}
x_1 = 3 \\
x_2 = - 1 \\
x_3 = 0 \\
x_4 = - 2 \\
\end{array} \right[/tex]