[1 2 5 8
2 3 0 5
3 0 6 9
0 4 7 11]
ive tried 4 times to reduce this but my answers all look different and wrong. any suggestions?
thanks..im done some row operations and right now my matrix looks like this
[1 -1 0 0
-1 7 1 7
1 0 2 3
0 0 1 1 ]
did you have that matrix at one point too, or should i just start over?
also, I have used about 10 row operations to get to that- is that too much? am i not seeing something really simple that could solve this using fewer row operations?
thanks.
Your row reducing seems rather random. I think it's best to have an order. Starting with
$\displaystyle
\left[ \begin{array}{cccc}
1 & 2 & 5 &8 \\
2& 3 & 0 &5\\
3 & 0 & 6 & 9\\
0 & 4 & 7 & 11 \end{array}\right]$ target to get rid of the red numbers $\displaystyle
\left[ \begin{array}{cccc}
1 & 2 & 5 &8 \\
\color{red}{2}& 3 & 0 &5\\
\color{red}{3} & 0 & 6 & 9\\
0 & 4 & 7 & 11 \end{array}\right]$
$\displaystyle
\begin{array}{c} 2R_1 -R_2 \rightarrow R_2\\
3R_1- R_3 \rightarrow R_3
\end{array}
$
$\displaystyle
\left[ \begin{array}{cccc}
1 & 2 & 5 &8 \\
0 & 1 & 10 &11\\
0 & 6 & 9 & 15\\
0 & 4 & 7 & 11 \end{array}\right]$ then use the second row to eliminate $\displaystyle
\left[ \begin{array}{cccc}
1 & 2 & 5 &8 \\
0 & 1 & 10 &11\\
0 & \color{red}{6} & 9 & 15\\
0 & \color{red}{4} & 7 & 11 \end{array}\right]$ etc