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The system of equations
$\begin{aligned} & \alpha x+y+z=\alpha-1 \\ & x+\alpha y+z=\alpha-1 \\ & x+y+\alpha z=\alpha-1\end{aligned}$
has no solution, if $\alpha$ is
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$\begin{aligned} & \alpha x+y+z=\alpha-1 \\ & x+\alpha y+z=\alpha-1 \\ & x+y+\alpha z=\alpha-1\end{aligned}$
has no solution, if $\alpha$ is
Solution:
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Verified Answer
The correct answer is:
-2
For no solution or infinitely many solutions $\left|\begin{array}{lll}\alpha & 1 & 1 \\ 1 & \alpha & 1 \\ 1 & 1 & \alpha\end{array}\right|=0 \Rightarrow \alpha=1, \alpha=-2$
But for $\alpha=1$, clearly there are infinitely many solutions and when we put $\alpha=-2$ in given system of equations and adding them together L.H.S $\neq$ R.H.S. i.e., No solution.
But for $\alpha=1$, clearly there are infinitely many solutions and when we put $\alpha=-2$ in given system of equations and adding them together L.H.S $\neq$ R.H.S. i.e., No solution.
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