The system of equations $ kx+y+z=1, x+k y+z=k $ and $ x+y+z k=k^{2} $ has no solution if $ k $ is equal to : [JEE Main 2021, 17 Mar (Shift 1)]

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The system of equations \( kx+y+z=1, x+k y+z=k \) and \( x+y+z k=k^{2} \) has no solution if \( k \) is equal to : [JEE …