If the system of equations
$\begin{array}{l}2\mathrm{x}-\mathrm{y}+\mathrm{z}=4\\ 5\mathrm{x}+\mathrm{\lambda y}+3\mathrm{z}=12\\ 100\mathrm{x}-47\mathrm{y}+\mathrm{\mu z}=212\end{array}$
has infinitely many solutions, then $\mathrm{\mu }-2\mathrm{\lambda }$ is equal to 

$\begin{array}{l}\begin{array}{rl} & \mathrm{\Delta }=0\Rightarrow \left|\begin{array}{ccc}2& -1& 1\\ 5& \mathrm{\lambda }& 3\\ 100& -47& \mathrm{\mu }\end{array}\right|=0\\ & 2(\mathrm{\lambda \mu }+141)+(5\mathrm{\mu }-300)-235-100\mathrm{\lambda }=0\dots \\ & {\mathrm{\Delta }}_3=0\Rightarrow \left|\begin{array}{ccc}2& -1& 4\\ 5& \mathrm{\lambda }& 12\\ 100& -47& 212\end{array}\right|=0\\ & 6\mathrm{\lambda }=-12\Rightarrow \mathrm{\lambda }=-2\end{array}\\ \text{ Put }\mathrm{\lambda }=2\text{ in (1) }\\ 2(-2\mathrm{\mu }+141)+5\mathrm{\mu }-300-235+200=0\\ \mathrm{\mu }=53\\ \therefore 57\end{array}$