Mathematics · 2023
JEE Main · 29 January 2023, Shift 1 · Q66
Let α and β be real numbers. Consider a 3 × 3 matrix A such that A^2=3 A+α I. If A^4=21 A+β I, then
Let $\displaystyle \alpha$ and $\displaystyle \beta$ be real numbers. Consider a $\displaystyle 3 \times 3$ matrix A such that $\displaystyle A^2=3 A+\alpha I$. If $\displaystyle A^4=21 A+\beta I$, then
Official answer
From NTA’s final answer key for this paper.
(3)
$\displaystyle \beta=-8$
More from Matrices and Determinants
- If α ≠ a, β ≠ b, γ ≠ c and |α, b, c; a, β, c; a, b, γ| =0, then a/(α-a)+b/(β-b)+(γ)/(γ-c) is equal to:2024
- 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
- Consider the matrices: A= [2, -5; 3, m], B= [20; m] and X= [x; y]. Let the set of all m, for which the system of equations A X=B has a negative…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= [2, -1; 1, 1]. If the sum of the diagonal elements of A^13 is 3^n, then n is equal to ____.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
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.