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 = &#8747; 0 1 / 2 x n x m - 1 d x , &#8704; n &#62; m and n , m &#8712; N . Consider a matrix A = a i j 3 &#215; 3 where a i j = J 6 + i , 3 - J i + 3 , 3 , i &#8804; j 0 , i &#62; j . Then adj A - 1 is :

Quantrex Academy · Accepted Answer

Correct answer: D. ( 105 ) 2 &#215; 2 38

&#8757; A = a 11 a 12 a 13 0 a 22 a 23 0 0 a 33 &#8658; A = a 11 a 22 a 33 &#8658; | A | = J 7 , 3 - J 4 , 3 &#183; J 8 , 3 - J 5 , 3 &#183; J 9 , 3 - J 6 , 3 = &#8747; 0 1 / 2 x 7 - x 4 x 3 - 1 d x &#183; &#8747; 0 1 / 2 x 8 - x 5 x 3 - 1 d x &#183; &#8747; 0 1 / 2 x 9 - x 6 x 3 - 1 d x = &#8747; 0 1 / 2 x 4 d x &#183; &#8747; 0 1 / 2 x 5 d x &#183; &#8747; 0 1 / 2 x 6 d x = 1 ( 210 ) &#183; ( 2 ) 18 Now adj A - 1 = A - 1 2 = 1 | A | 2 = ( 210 ) &#183; 2 18 2 = ( 105 ) 2 &#183; ( 2 ) 38

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 :

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Step-by-step solution

More from Definite Integration

Let J n , m = &#8747; 0 1 / 2 x n x m - 1 d x , &#8704; n &#62; m and n , m &#8712; N . Consider a matrix A = a i j 3 &#215; 3 where a i j = J 6 + i , 3 - J i + 3 , 3 , i &#8804; j 0 , i &#62; j . Then adj A - 1 is :

Options

Correct answer

Step-by-step solution

More from Definite Integration

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 :