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NDA2018MathematicsDeterminantsActual

What is the determinant of the matrix ( array ccc x & y & y+z z & z & z+x y & z & x+y array ) ?

Options

  1. A(x-y)(y-z)(z-x)
  2. B( x - z )( z - x )
  3. C( y - z )( z - x )
  4. D(z-x)^2(x+y+z)

Correct answer

D. (z-x)^2(x+y+z)

Step-by-step solution

| array lll x & y & y+z z & x & z+x y & z & x+y array |= R ₁ R ₁+ R ₂+ R ₃ | array ccc x+y+z & x+y+z & 2(x+y+z) z & x & z+x y & z & x+y array | aligned & =(x+y+z) | array ccc 1 & 1 & 2 z & x & z+x y & z & x+y array | & =(x+y+z)(z+x)^2,( replacing z by x) aligned

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