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AP EAMCET2015MathematicsDeterminants

The value of the determinant | array lll b^2-a b & b-c & b c-a c a b-a^2 & a-b & b^2-a b b c-a c & c-a & a b-a^2 array | is

Options

  1. Aabc
  2. Ba+b+c
  3. C0
  4. Dab + bc + ca

Correct answer

C. 0

Step-by-step solution

aligned & Let D = | array lll b^2-a b & b-c & b c-a c a b-a^2 & a-b & b^2-a b b c-a c & c-a & a b-a^2 array | & = | array lll b(b-a) & b-c & c(b-a) a(b-a) & a-b & b(b-a) c(b-a) & c-a & a(b-a) array | & =(b-a)(b-a) | array lll b & b-c & c a & a-b & b c & c-a & a array | aligned =(b-a)^2 | array ccc b & 0 & c a & 0 & b c & 0 & a array | [ using C₂ C₂- (C₁-C₃ ) ]=0

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