solving system of linear equations

[pxy2d1]

L = lambda

x + 2y + Lz = 0
2x + 3y -2z = L
Lx + y + z = 3

in other problems like this i have solved using gaussion elimination where i would have used x in equation one as a pivot to get rid of the x's in the other two equations.
however the lambda in the equation has me stumped. how would i use the x to get rid of the Lx.
any help would be greatly appreciated
is there other methods for solving this problem
thanks

 

[galactus]

Ax=b

\(\displaystyle \L\\\begin{bmatrix}1&2&{\lambda}\\2&3&-2\\{\lambda}&1&1\end{bmatrix}\cdot\begin{vmatrix}x\\y\\z\end{vmatrix}=\begin{bmatrix}0\\1\\3\end{bmatrix}\)

x=\(\displaystyle A^{-1}b\)

If you multiply the inverse of your matrix times b, you should get x,y,z in terms of lambda alone.

 

[pka]