AP EAMCET201923 Apr 2019Morning ShiftMathematicsDeterminantsActual
The equation obtained by eliminating (a, b, c ) from the equations (x= a b-c , y= b c-a ), (z= c a-b ) is
Options
- A( | array lll 1 & -x & x 1 & -y & y 1 & -z & z array |=0 )
- 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 )
- D( | array lll x & y & 1 y & x & 1 1 & x & y array |=0 )
Correct answer
B. ( | array ccc 1 & -x & x 1 & 1 & -y 1 & z & 1 array |=0 )
Step-by-step solution
Given equations ( gathered x= a b-c a-b x+c x=0 y= b c-a a y+b-c y=0 gathered ) and ( z= c a-b a z-b z-c=0 ) Now, on eliminating (a, b, c ) from the above equations, we get ( | array ccc 1 & -x & x y & 1 & -y z & -z & -1 array |=0 ) On applying (C₁ C₁+C₂+C₃ ), we get ( | array ccc 1 & -x & x 1 & 1 & -y -1 & -z & -1 array |=0 | array ccc 1 & -x & x 1 & 1 & -y 1 & z & 1 array |=0 ) Hence, option (b) is correct.