Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsMatricesPractice

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 )

Options

  1. A7
  2. B8
  3. C25 3
  4. D9

Correct answer

B. 8

Step-by-step solution

∵ 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

Practice Matrices on Quantrex Academy →

More from Matrices

Which one of the following matrices can be obtained by performing elementary row transformations on the 3 3 identity matrix? 2026Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be integers such that M²⁶ = bmatrix p & q r & s bmatrix and _ k=1 ²⁶ M^k = bmatrix a & b c & d 2026For real numbers , , , and , consider the matrix M = bmatrix & 1 2 & - 1 2 1 3 & & 1 3 & & bmatrix . Suppose that MM^T = I , where M^T is the transpose of the matrix M , and I is t 2026Let R denote the set of all real numbers and let i = -1 . Consider the matrices S = bmatrix 0 & -1 1 & 0 bmatrix and T = bmatrix 1 & 1 0 & 1 bmatrix . Let a, b, c, d be real number 2026Let A = bmatrix & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 bmatrix + adj (A) . If (B)=66 , then ( adj (A)) equals: 2026Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 i, j 3 . If B = A⁹⁹ - I , then the value of b₃₁ - b₂₁ b₃₂ is : 2026Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + (adj(adj(A))) + (adj(A)(adj(adj(A)))) = bmatrix 2 & -2 & 2 -2 & 0 & -1 0 & 0 & -1 bmatrix for some , R . Then 2026Let M be a 3 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix and M pmatrix 0 0 1 pmatrix = pmatrix -1 1 1 pmatr 2026 Full Matrices list All NTA Abhyas JEE Main PYQs