The system of equations is Determine the values of corresponding to each of the…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The system of equations is λx+y+z=2,x+λy+z=2,x+y+λz=2.\begin{aligned}\lambda x+y+z&=2,\\x+\lambda y+z&=2,\\x+y+\lambda z&=2.\end{aligned} Determine the values of λ\lambda corresponding to each of the following cases: (i) The system has a unique solution. (ii) The system has infinitely many solutions. (iii) The system is inconsistent (no solution).

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