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

Step-by-step solution

∵ 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 .