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Questions › CUET-PG › CUET-PG 2023 Shift 1 › Q88
4 marks, −1Mathematics › Matrices, determinants and linear systems › Matrix operations and special matricesModerateabout 2 min

CUET-PG 2023 Shift 1 Question 88: Matrices, determinants and linear systems

Let A=(p−qqp)A = \begin{pmatrix} p & -q \\ q & p \end{pmatrix}A=(pq​−qp​) be a 2 x 2 matrix. (A) The rank of matrix A given by r(A) is 3 (B) Matrix A is orthogonal if and only if p2+q2=1p^2 + q^2 = 1p2+q2=1 (C) Transpose of matrix A is given by AT=(pq−qp)A^T = \begin{pmatrix} p & q \\ -q & p \end{pmatrix}AT=(p−q​qp​) (D) Determinant of matrix A is ∣A∣=p|A| = p∣A∣=p Choose the most appropriate answer from the options given below:

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Let A = [p -q; q p] be a 2 x 2 matrix. (A) The rank of matrix A given by r(A) is 3 (B) Matrix A is orthogonal if and only if p² + q² = 1 (C) Transpose of matrix A is given by Aᵀ = [p q; -q p] (D) Determinant of matrix A is |A| = p Choose the most appropriate answer from the options given below: (A) A and B only (B) A and C only (C) B and C only (D) A and D only

Also written as: Let A = [p -q; q p] be a 2 x 2 matrix. (A) The rank of matrix A given by r(A) is 3 (B) Matrix A is orthogonal if and only if p^2 + q^2 = 1 (C) Transpose of matrix A is given by A^T = [p q; -q p] (D) Determinant of matrix A is |A| = p Choose the most appropriate answer from the options given below:

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Matrix operations and special matrices, part of Matrices, determinants and linear systems in Mathematics.

Adding, multiplying and transposing matrices, and the matrices with special properties.

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Question from the CUET-PG 2023 Shift 1 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.