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

Question

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, 0, 2 K, K, K 2

MARKS App · Accepted Answer

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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