Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i , j = 1 , 2 , 3 . Then, the matrix A 2 + A 3 + … + A 10 is equal to

Question

Let A = a i j be a square matrix of order 3 such that a i j = 2 j - i , for all i , j = 1 , 2 , 3 . Then, the matrix A 2 + A 3 + … + A 10 is equal to, 3 10 - 1 2 A, 3 10 + 1 2 A, 3 10 + 3 2 A, 3 10 - 3 2 A

MARKS App · Accepted Answer

Given, A = a i j 3 × 3 where a i j = 2 j - i we get, A = 1 2 4 1 2 1 2 1 4 1 2 1 A 2 = 1 2 4 1 2 1 2 1 4 1 2 1 1 2 4 1 2 1 2 1 4 1 2 1 ⇒ A 2 = 3 6 12 3 2 3 6 3 4 3 2 3 = 3 A ⇒ A 3 = 3 A 2 = 9 A Now, A 2 + A 3 + A 4 + ⋯ A 10 = 3 A + 3 2 A + 3 3 A + ⋯ 3 9 A = 3 A 3 9 - 1 3 - 1 = A 3 10 - 3 2

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