NDA2017MathematicsDeterminantsActual
What is the value of the determinant? | array ccc 1 & 1 & 1 1 & 1+ xyz & 1 1 & 1 & 1+ xyz array | ?
Options
- A1+x+y+z
- B2 x y z
- Cx^2 y^2 z^2
- D2 x^2 y^2 z^2
Correct answer
C. x^2 y^2 z^2
Step-by-step solution
aligned & | array ccc 1 & 1 & 1 1 & 1+ xyz & 1 1 & 1 & 1+ xyz array | array c c₂ c₂-c₁ c₃ c₃-c₁ array & = | array ccc 1 & 0 & 0 1 & x y z & 0 1 & 0 & x y z array |=1 (x^2 y^2 z^2-0 )=x^2 y^2 z^2 aligned