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Manipal MET2010MathematicsDeterminants

For positive numbers x, y, z the numerical value of the determinant | array ccc 1 & _x y & _x z _y x & 1 & _y z _z x & _z y & 1 array | is

Options

  1. A0
  2. B1
  3. C2
  4. DNone of these

Correct answer

A. 0

Step-by-step solution

We have, | array ccc 1 & _x y & _x z _y x & 1 & _y z _z x & _z y & 1 array |= | array ccc 1 & y x & z x x y & 1 & z y x z & y z & 1 array |= 1 x y z | array lll x & y & z x & y & z x & y & z array |=0[ all rows are identical]

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