Let P n be a square matrix of order 3 such that P n = a i j , where a i j = 3 i + j 4 2 n for 1 ≤ i ≤ 3, 1 ≤ j ≤ 3 . Then the value of l i m n → ∞ T r 4 P 1 + 4 2 P 2 . . . . . 4 n P n is (where T r A denotes trace of matrix A i.e sum of principal diagonal elements of A )

Question

Let P n be a square matrix of order 3 such that P n = a i j , where a i j = 3 i + j 4 2 n for 1 ≤ i ≤ 3, 1 ≤ j ≤ 3 . Then the value of l i m n → ∞ T r 4 P 1 + 4 2 P 2 . . . . . 4 n P n is (where T r A denotes trace of matrix A i.e sum of principal diagonal elements of A ), 7, 8, 25 3, 9

MARKS App · Accepted Answer

∵ P n = 3 i + j 4 2 n = 1 4 2 n 3 i + j 4 n P n = 1 4 n 3 i + j T r 4 P 1 + 4 2 P 2 . . . 4 n P n = T r 4 P 1 + T r 4 2 P 2 . . . . + T r 4 n P n = 24 4 + 24 4 2 . . . . . . . . . 24 4 n l i m n → ∞ T r 4 P 1 + 4 2 P 2 . . . . + 4 n P n l i m n → ∞ 24 4 + 24 4 2 . . . . . . . 24 4 n = 6 1 - 1 4 = 8

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