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Manipal MET2014MathematicsDeterminants

The value of the determinant | array ccc (a^x+a^ -x )^2 & (a^x-a^ -x )^2 & 1 (b^x+b^ -x )^2 & (b^x-b^ -x )^2 & 1 (c^x+c^ -x )^2 & (c^x-c^ -x )^2 & 1 array | is

Options

  1. A0
  2. B2 a b c
  3. Ca^2 b^2 c^2
  4. DNone of these

Correct answer

A. 0

Step-by-step solution

Given determinant is = | array ccc (a^x+a^ -x )^2 & (a^x-a^ -x )^2 & 1 (b^x+b^ -x )^2 & (b^x-b^ -x )^2 & 1 (c^x+c^ -x )^2 & (c^x-c^ -x )^2 & 1 array | Applying C₁ C₁-C₂ , we get aligned & = | array ccc 4 & (a^x-a^ -x )^2 & 1 4 & (b^x-b^ -x )^2 & 1 4 & (c^x-c^ -x )^2 & 1 array |=4 | array ccc 1 & (a^x-a^ -x )^2 & 1 1 & (b^x-b^ -x )^2 & 1 1 & (c^x-c^ -x )^2 & 1 array | & =0 ( two columns are identical) aligned

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