jee_main_2024_30_january_evening - Matrices and Determinants Topics

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QUESTION #1 System of Linear Equations
Consider the system of linear equations x + y + z = 5, x + 2 y + λ^ 2 z = 9, x + 3y + λ z = μ , where λ ,μ in R . Then, which of the following statement is NOT correct?
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QUESTION #20 Properties of Matrices
Let R = pmatrix x & 0 & 0 0 & y & 0 0 & 0 & z pmatrix be a non-zero 3 × 3 matrix, where x θ = y (θ +(2π)/(3)) = z (θ +(4π)/(3)) ≠ 0, θ in (0,2π). For a square matrix M, let trace (M) denote the sum of all the diagonal 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. Choose the correct statement:
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Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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