Characteristic Equation and Cayley-Hamilton Theorem

JEE Main Mathematics · Matrices and Determinants · 11 questions, latest first

• Let A= [1, 2, 7; 4, -2, 8; 3, 8, -7] and det(A-α I)=0, where α is a real number. If the largest possible value of α is p, then…20264 April, Shift 2 · Q6
• Let S={A= [a, b; c, d]: a, b, c, d ∈{0,1,2,3,4}. and.A^2-4 A+3 I=0} be a set of 2 × 2 matrices. Then the number of matrices in S,…20264 April, Shift 1 · Q5
• Let A= [1, 2; 1, α] and B= [3, 3; β, 2]. If A^2-4 A+I=O and B^2-5 B-6 I=O, then among the two statements: (S1): [(B-A)(B+A)]^T=…20262 April, Shift 1 · Q4
• If A= [2, 3; 3, 5], then the determinant of the matrix (A^2025-3 A^2024+A^2023) is202622 January, Shift 1 · Q4
• For some α, β ∈ R, let A= [α, 2; 1, 2] and B= [1, 1; 1, β] be such that A^2-4 A+2 I=B^2-3 B+I=O. Then (det(adj(A^3-B^3)))^2 is…202621 January, Shift 1 · Q21
• Let B= [1, 3; 1, 5] and A be a 2 × 2 matrix such that A B^-1=A^-1. If B C B^-1=A and C^4+α C^2+β I=O, then 2 β-α is equal to20249 April, Shift 2 · Q4
• Let A= [2, a, 0; 1, 3, 1; 0, 5, b]. If A^3=4 A^2-A-21 I, where I is the identity matrix of order 3 × 3, then 2 a+3 b is equal to20248 April, Shift 1 · Q4
• Let A be a 2 × 2 symmetric matrix such that A [1; 1] = [3; 7] and the determinant of A be 1. If A^-1=α A+β I, where I is an…20244 April, Shift 2 · Q23
• Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements is -3. If the points (x, y) satisfying…20244 April, Shift 1 · Q27
• 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…202427 January, Shift 2 · Q22
• If A= [1, 5; λ, 10], A^-1=α A+β I and α+β=-2, then 4 α^2+β^2+λ^2 is equal to:20238 April, Shift 2 · Q4