The value of |α| for which the system of equation αx+y+z=α−1,x+αy+z=α−1,x+y+αz=α−1 has no solution, is ..............
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Solution
Augumented matrix is ⎡⎢⎣α11α−11α1α−111αα−1⎤⎥⎦ given system of equations has no solution. ⇒Δ=0 and Δx≠0 Δx=∣∣
∣∣α−111α−1α1α−11α∣∣
∣∣=(α−1)3≠0 ⇒α≠1 Δ=∣∣
∣∣α111α111α∣∣
∣∣=(α+2)(α−1)2=0 ⇒α=−2 (∵α≠1) ∴|α|=2