JEE Main 2024 Mathematics question
Let be a non-zero 3 × 3 matrix, where x sinθ = y sin(θ + 2π/3) = z sin(θ + 4π/3) ≠ 0, θ ∈ (0, 2π). For a square matrix M, let trace (M) denote the sum of all the diagonals entries of M. Then, among the statements: (I) Trace (R) = 0 (II) If trace (adj(adj(R))) = 0, then R has exactly one non-zero entry.
Answer: (D)
Solution
From the given relation y = x sinθ/sin(θ + 2π/3) and z = x sinθ/sin(θ + 4π/3), so x + y + z = −3x/[4 sin(θ + 2π/3) sin(θ + 4π/3)] ≠ 0, so (I) is false. For a
See the full step-by-step solution
Create a free account to read the complete working, and practise questions like this in a timed test.
Create a free account