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AP EAMCET202125 Aug 2021Morning ShiftMathematicsDeterminantsActual

If _k= | array ccc 1 & 0 & 0 0 & k & k-1 0 & k-1 & k array | , then ₁+ ₂+ + ₂₀ is equal to

Options

  1. A200
  2. B40
  3. C0
  4. D400

Correct answer

D. 400

Step-by-step solution

We have, aligned _K & = | array ccc 1 & 0 & 0 0 & k & k-1 0 & k-1 & k array | _K & =k^2-(k-1)^2 ₁+ ₂+ ₃ & + + ₂₀ & = (1^2-0^2 )+ (2^2-1^2 )+ (20^2-19^2 ) & =20^2=400 aligned

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