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COMEDK2016MathematicsDeterminants

The value of | array ccc x+y & y+z & z+x x & y & z x-y & y-z & z-x array |=

Options

  1. A0
  2. B(x+y+z)³
  3. C2(x+y+z)³
  4. D2(x+y+z)²

Correct answer

A. 0

Step-by-step solution

| array ccc x+y & y+z & z+x x & y & z x-y & y-z & z-x array | aligned =& | array ccc 2(x+y+z) & y+z & z+x (x+y+z) & y & z 0 & y-z & z-x array | & [ C₁ C₁+C₂+C₃ ] aligned =(x+y+z) | array lcc 2 & y+z & z+x 1 & y & z 0 & y-z & z-x array |=(x+y+z) | array lll 2 & y+z & z+x 0 & y-z & z-x 0 & y-z & z-x array | [ R_ i₂ 2 R₂-R₁ ]=(x+y+z) 0=0 [ R₂ . and R₃ are identical ]

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