Transpose, Symmetric and Skew-Symmetric Matrices

JEE Main Mathematics · Matrices and Determinants · 6 questions, latest first

• Let A be a 3 × 3 matrix such that A+A^T=O. If A [1; -1; 0] = [3; 3; 2], A^2 [1; -1; 0] = [-3; 19; -24] and det(adj(2 adj(…202622 January, Shift 1 · Q22
• Let A be a 3 × 3 matrix such that X^T AX=O for all nonzero 3 × 1 matrices X= [x; y; z]. If A [1; 1; 1] = [1; 4; -5], A [1; 2; 1]…202524 January, Shift 1 · Q22
• Let A be a 2 × 2 matrix with real entries such that A^′=α A+I, where α ∈ R-{-1,1}. If det(A^2-A)=4, then the sum of all possible…202311 April, Shift 1 · Q6
• If P is a 3 × 3 real matrix such that P^T=a P+(a-1) I, where a>1, then202330 January, Shift 2 · Q64
• Let A be a symmetric matrix such that |A|=2 and [2, 1; 3, 3/2] A= [1, 2; α, β]. If the sum of the diagonal elements of A is s,…202329 January, Shift 2 · Q83
• Let A, B, C be 3 × 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements (S1) A^13…202325 January, Shift 2 · Q65