Mathematics · 2024
JEE Main · 8 April 2024, Shift 1 · Q22
Let A= [2, -1; 1, 1]. If the sum of the diagonal elements of A^13 is 3^n, then n is equal to ____.
Let $\displaystyle A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$. If the sum of the diagonal elements of $\displaystyle A^{13}$ is $\displaystyle 3^n$, then $\displaystyle n$ is equal to
$\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
7
More from Matrices and Determinants
- Consider the matrix f(x)= [cos x, - sin x, 0; sin x, cos x, 0; 0, 0, 1]. Given below are two statements: Statement I: f(-x) is the inverse of the…2024
- Let A be a 3 × 3 real matrix such that A (1; 0; 1) =2 (1; 0; 1), A (-1; 0; 1) =4 (-1; 0; 1), A (0; 1; 0) =2 (0; 1; 0). Then, the system (A-3 I) (x;…2024
- Let A= [1, 1, 2; -2, 0, 1; 1, 3, 5]. Then the sum of all elements of the matrix adj(adj(2(adj A)^-1)) is equal to:2026
- Let A be a 3 × 3 matrix of non-negative real elements such that A [1; 1; 1] =3 [1; 1; 1]. Then the maximum value of det(A) is ____.2024
- Let A be a 2 × 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A-x I|=0 be -1 and 3, then the sum of the…2024
- For some a, b, let f(x)= |a+(sin x)/x, 1, b; a, 1+(sin x)/x, b; a, 1, b+(sin x)/x|, x ≠ 0, lim_x → 0 f(x)=λ+μ a+ν b. Then (λ+μ+ν)^2 is equal to:2025
- If the system of equations 2 x+λ y+3 z=5; 3 x+2 y-z=7; 4 x+5 y+μ z=9 has infinitely many solutions, then (λ^2+μ^2) is equal to:2025
- Let A= [1, 0, 0; 0, α, β; 0, β, α] and |2 A|^3=2^21 where α, β ∈ Z, Then a value of α is2024
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.