Let J n , m = ∫ 0 1 / 2 x n x m - 1 d x , ∀ n m and n , m ∈ N . Consider a matrix A = a i j 3 × 3 where a i j = J 6 + i , 3 - J i + 3 , 3 , i ≤ j 0 , i j . Then adj A - 1 is :

Question

Let J n , m = ∫ 0 1 / 2 x n x m - 1 d x , ∀ n > m and n , m ∈ N . Consider a matrix A = a i j 3 × 3 where a i j = J 6 + i , 3 - J i + 3 , 3 , i ≤ j 0 , i > j . Then adj A - 1 is :, ( 15 ) 2 × 2 34, ( 15 ) 2 × 2 42, ( 105 ) 2 × 2 36, ( 105 ) 2 × 2 38

MARKS App · Accepted Answer

∵ A = a 11 a 12 a 13 0 a 22 a 23 0 0 a 33 ⇒ A = a 11 a 22 a 33 ⇒ | A | = J 7 , 3 - J 4 , 3 · J 8 , 3 - J 5 , 3 · J 9 , 3 - J 6 , 3 = ∫ 0 1 / 2 x 7 - x 4 x 3 - 1 d x · ∫ 0 1 / 2 x 8 - x 5 x 3 - 1 d x · ∫ 0 1 / 2 x 9 - x 6 x 3 - 1 d x = ∫ 0 1 / 2 x 4 d x · ∫ 0 1 / 2 x 5 d x · ∫ 0 1 / 2 x 6 d x = 1 ( 210 ) · ( 2 ) 18 Now adj A - 1 = A - 1 2 = 1 | A | 2 = ( 210 ) · 2 18 2 = ( 105 ) 2 · ( 2 ) 38

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