The greatest value of c ∈ R for which the system of linear equations x - c y - c z = 0 , c x - y + c z = 0 , c x + c y - z = 0 has a non-trivial solution, is

Question

The greatest value of c ∈ R for which the system of linear equations x - c y - c z = 0 , c x - y + c z = 0 , c x + c y - z = 0 has a non-trivial solution, is, - 1, 2, 1 2, 0

MARKS App · Accepted Answer

∵ System of equation has non trivial solution. It is possible only when ∆ = 0 . ∴ ∆ = 1 - c - c c - 1 c c c - 1 = 0 ⇒ 1 1 - c 2 + c - c - c 2 - c c 2 + c = 0 ⇒ 2 c 3 + 3 c 2 - 1 = 0 ⇒ c = - 1 , 1 2 Hence, the greatest value of c = 1 2 .

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