Let A = a i j be a 3 × 3 matrix where a i j = i j - j i + 2 i j x i < j 1 i > j 0 i = j , then the minimum value of A is equal to (where x is a real number)

Step-by-step solution

A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 a 11 = 0 , a 12 = 3 x , a 13 = 4 x , a 21 = 1 a 22 = 0 , a 23 = 11 x , a 31 = 1 , a 32 = 1 , a 33 = 0 A = 0 3 x 4 x 1 0 11 x 1 1 0 &#8658; A = 33 x 2 + 4 x Minimum value of A = - 4 33