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AP EAMCET201921 Apr 2019Evening ShiftMathematicsMatricesActual

If A = p q r r p q q r p and A A T = I , then p 3 + q 3 + r 3 =

Options

  1. A± 1
  2. Bp q r
  3. C3 p q r
  4. D3 p q r ± 1

Correct answer

D. 3 p q r ± 1

Step-by-step solution

It is given that, A A ⊤ = I It is an orthogonal matrix and the determinant of orthogonal matrix is ± 1   . . p q r r p q q r p = ± 1 Solve the above determinant, p 3 - p q r - p q r - p q r + q 3 + r 3 = ± 1 ⇒ p 3 + q 3 + r 3 - 3 p q r = ± 1 ⇒ p 3 + q 3 + r 3 = 3 p q r ± 1

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