Let A be a symmetric matrix such that A = 2 and 2 1 3 3 2 A = 1 2 α β If the sum of the diagonal elements of A is s , then β s α 2 is equal to _________.

Step-by-step solution

Let A = a b b c And, 2 1 3 3 2 A = 1 2 α β ⇒ 2 1 3 3 2 a b b c = 1 2 α β ⇒ 2 a + b 2 b + c 3 a + 3 b 2 3 b + 3 c 2 = 1 2 α β So, 2 a + b = 1 2 b + c = 2 So, 4 a - c = 0       . . . . i Also, A = 2 ⇒ a c - b 2 = 2 ⇒ a 4 a - 1 - 2 a 2 = 2 ⇒ 4 a 2 - 4 a 2 - 1 + 4 a = 2 ⇒ a = 3 4 ⇒ b = 1 - 2 a = 1 - 6 4 = - 1 2 c = 4 a = 3 And, 3 a + 3 b 2 = α ⇒ α = 9 4 - 3 4 = 3 2 3 b + 3 c 2 = β ⇒ β = - 3 2 + 9 2 = 3