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KCET2016MathematicsDeterminants

If ( x y z ) are not equal and ( 0, 1 ) the value of ( | array ccc x & y & z 2 x & 2 y & 2 z 3 x & 3 y & 3 z array | ) is equal to

Options

  1. A( (x y z) )
  2. B( (6 y z) )
  3. C( 00 )
  4. D( (x+y+z) )

Correct answer

C. ( 00 )

Step-by-step solution

Given that, x, y, z 0 1 As we know, 2 x- x= 2 and 3 x- x= 3 Given that | array ccc x & y & z 2 x & 2 y & 2 z 3 x & 3 y & 3 z array |R₂ R₂-R₁ and R₃ R₃-R₁ array ll x & y & z 2 & 2 & 2 3 & 3 & 3 & = & 2 3 When the two rows of determinants are identical the value of determinant is equal to 0 & array ccc x & y & z 1 & 1 & 1 1 & 1 & 1 array array

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