Question : Solve the equations
2x + 3y+z=9
x+2y+3z=6
3x+y+2z=8
by factorization method
I don't know of the method you are speaking of but you can solve it as follows
$\displaystyle
\left[ \begin{array}{c}
x\\
y\\
z\end{array}\right]=\left[ \begin{array}{ccc}
2 & 3 & 1 \\
1 & 2 & 3 \\
3 & 1 & 2 \end{array} \right]^{-1} \left[ \begin{array}{c}
9\\
6\\
8\end{array}\right]
$
To finish with the method posted you need to find this
$\displaystyle
\left[ \begin{array}{ccc}
2 & 3 & 1 \\
1 & 2 & 3 \\
3 & 1 & 2 \end{array} \right]^{-1}
$
which is the inverse of a $\displaystyle 3\times 3$ matrix, read this
Cramer's rule - Wikipedia, the free encyclopedia
the result needs to be mulitplied by
$\displaystyle \left[ \begin{array}{c}
9\\
6\\
8\end{array}\right]$
do you know how to multiply matrices?
Read this, Matrix multiplication - Wikipedia, the free encyclopedia
or try this Matrix Multiplying Calculator
Good luck!