The value of u for which the system of equation $\begin{array}{r}\mathrm{\alpha x}+\mathrm{y}+\mathrm{z}=\mathrm{\alpha }-1\\ \mathrm{x}+\mathrm{\alpha y}+\mathrm{z}=\mathrm{\alpha }-1\\ \mathrm{x}+\mathrm{y}+\mathrm{\alpha z}=\mathrm{\alpha }-1\end{array}$ has no solution, is -----------

System of equations

$\begin{array}{r}\mathrm{\alpha x}+\mathrm{y}+\mathrm{z}=\mathrm{\alpha }-1---\left(1\right)\\ \mathrm{x}+\mathrm{\alpha y}+\mathrm{z}=\mathrm{\alpha }-1----\left(2\right)\\ \mathrm{x}+\mathrm{y}+\mathrm{\alpha z}=\mathrm{\alpha }-1----\left(3\right)\end{array}$

Since system has no solution. Therefore, (1) $\mathrm{\Delta }=0\text{ and }\left(2\right)\mathrm{\alpha }-1\ne 0$

$\begin{array}{l}\left|\begin{array}{ccc}\mathrm{\alpha }& 1& 1\\ 1& \mathrm{\alpha }& 1\\ 1& 1& \mathrm{\alpha }\end{array}\right|=0,\mathrm{\alpha }\ne 1\\ {\mathrm{R}}_1\to {\mathrm{R}}_1-{\mathrm{R}}_3,{\mathrm{R}}_2\to {\mathrm{R}}_2\to {\mathrm{R}}_3\\ \left|\begin{array}{ccc}\mathrm{\alpha }-1& 0& 1-\mathrm{\alpha }\\ 0& \mathrm{\alpha }-1& 1-\mathrm{\alpha }\\ 1& 1& \mathrm{\alpha }\end{array}\right|=0\\ \text{ or }(\mathrm{\alpha }-1)\left[\mathrm{\alpha }\right(\mathrm{\alpha }-1)-(1-\mathrm{\alpha }\left)\right]+(1-\mathrm{\alpha })[-(\mathrm{\alpha }-1\left)\right]=0\end{array}$

$\begin{array}{l}\mathrm{or} (\mathrm{\alpha }-1)\left[\mathrm{\alpha }\right(\mathrm{\alpha }-1)+(\mathrm{\alpha }-1\left)\right]+(\mathrm{\alpha }-1{)}^2=0\\ \mathrm{or} (\mathrm{\alpha }-1{)}^2[(\mathrm{\alpha }+1)+1]=0\\ \mathrm{or} \mathrm{\alpha }=1,1,-2\text{ or }\mathrm{\alpha }=1,-2\end{array}$

Since system has no solution , $\alpha \ne 1$

$\therefore \alpha =-2$