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Question

The value of |α| for which the system of equation αx+y+z=α1,x+αy+z=α1,x+y+αz=α1 has no solution, is ..............

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Solution

Augumented matrix is α11α11α1α111αα1
given system of equations has no solution.
Δ=0 and Δx0
Δx=∣ ∣α111α1α1α11α∣ ∣=(α1)30
α1
Δ=∣ ∣α111α111α∣ ∣=(α+2)(α1)2=0
α=2 (α1)
|α|=2

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