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COMEDK2014MathematicsDeterminants

| array ccc 1 & 1 & 1 a & b & c a²-b c & b²-c a & c²-a b array | is equal to

Options

  1. A0
  2. B1
  3. Ca b c
  4. D(a-b)(b-c)(c-a)

Correct answer

A. 0

Step-by-step solution

Let = | array ccc 1 & 1 & 1 a & b & c a²-b c & b²-c a & c²-a b array | On applying C₃ C₃-C₂ and C₂ C₂-C₁ , we get aligned =& | array ccc 1 & 0 & 0 a & b-a & c-b a²-b c & +c(b-a) & +a(c-b) array | =& 1[(b-a)(c-b)(c+b+a) &-(c-b)(b-a)(b+a+c)]=0 aligned

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