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AP EAMCET202120 Aug 2021Evening ShiftMathematicsDeterminantsActual

If k ∈ R and det A = a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 = K then det B = a 1 b 1 c 1 a 2 + 2 a 1 b 2 + 2 b 1 c 2 + 2 c 1 a 3 b 3 c 3 is equal to

Options

  1. A0
  2. B2   K
  3. CK
  4. DK 2

Correct answer

C. K

Step-by-step solution

det A = a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 = K d e t B = a 1 b 1 c 1 a 2 + 2 a 1 b 2 + 2 b 1 c 2 + 2 c 1 a 3 b 3 c 3 R 2 → R 2 - 2 R 1 d e t B = a 1 b 1 c 1 a 2 + 2 a 1 - 2 a 1 b 2 + 2 b 1 - 2 b 1 c 2 + 2 c 1 - 2 c 1 a 3 b 3 c 3 d e t B = a 1 b 1 c 1 a 2     b 2     c 2 a 3 b 3 c 3 d e t B = K

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