Let R = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ z 0 0 0 y 0 0 0 x be a non-zero 3 × 3 matrix, where xsin θ = ysin ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + θ 3 2 = zsin ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + θ 3 4 ≠ 0, θ ∈ (0, 2 π ). For a square matrix M, let trace (M) denote the sum of all the diagonals entries of M. Then, among the statements: (I) Trace

Question

Let R = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ z 0 0 0 y 0 0 0 x be a non-zero 3 × 3 matrix, where xsin θ = ysin ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + θ 3 2 = zsin ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + θ 3 4 ≠ 0, θ ∈ (0, 2 π ). 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.

Accepted Answer

Neither (I) nor (II) is true CAREER POINT CAREER POINT Ltd., CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 081-47250011 www.careerpoint.ac.in 24 JEE Main Online Paper

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