Eliminating a, b, c from x= a b-c , y= b c-a , z= c a-b , we get

Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants

1. \[\left|\begin{array}{ccc} 1 & -x & x \\ -y & 1 & y \\ 1 & -z & z \end{array}\right|\] = 0
2. \[\left|\begin{array}{ccc} 1 & -x & x \\ 1 & 1 & -y \\ 1 & z & 1 \end{array}\right|\] = 0
3. \[\left|\begin{array}{ccc} 1 & -x & x \\ y & 1 & -y \\ -z & z & 1 \end{array}\right|\] = 0
4. none of these

Answer

(B) | array ccc 1 & -x & x 1 & 1 & -y 1 & z & 1 array | = 0, (C) | array ccc 1 & -x & x y & 1 & -y -z & z & 1 array | = 0

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