The matrix , where is the transpose of , and , . Then equals:
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DSE 2019 Question 20: Matrices, determinants and linear systems
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The matrix Q=PAPᵀ, where Pᵀ is the transpose of P, and P=[√3/2 1/2; -1/2 √3/2], A=[1 1; 0 1]. Then PᵀQ¹²P equals: (A) [1 0; 144 1] (B) [1 144; 0 1] (C) [2+√3 1; -1 2-√3] (D) [1 12; 0 1]
Also written as: The matrix Q=PAP^T, where P^T is the transpose of P, and P=[sqrt(3)/2 1/2; -1/2 sqrt(3)/2], A=[1 1; 0 1]. Then P^TQ^(12)P equals:
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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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