The system αx + y + z = α − 1 , x + α y + z = α − 1 , x + y + α z = α − 1 has no solution. How many values of α are possible?

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The coefficient determinant is ( α + 2 ) ( α − 1 ) 2 . At α = 1 there are infinitely many solutions; at α = − 2 the system is inconsistent. Thus one value works.

Mathematics - Matrices Question with Solution | TestHub

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