Consider the system of equations a x + y + b z = 0 ,   b x + y + a z = 0 and a x + b y + a b z = 0 where a , b ∈ 0,1 , 2 , 3,4 . The number of ordered pairs a , b for which the system has non-trivial solutions is

Step-by-step solution

For non-trivial solutions, a 1 b b 1 a a b a b = 0 ⇒ a - b a - b 2 = 0 ⇒ Either a = b or a = b 2 When a = b , then ordered pairs are 0,0 , 1,1 , 2,2 , 3,3 , 4,4 When a = b 2 , then 4 , 2 Hence, number of ordered pairs are 6