If x= a b-c , y= b c-a , z= c a-b then what is the value of the following? | array ccc 1 & -x & x 1 & 1 & -y 1 & z & 1 array |

Step-by-step solution

| array ccc 1 & -x & x 1 & 1 & -y 1 & z & 1 array | Applying R ₂ R ₂- R ₁ and R ₃ R ₃- R ₁ aligned & = | array ccc 1 & -x & x 0 & 1+x & -y-x 0 & z+x & 1-x array | & =1+x y+y z+z x aligned array r =1+ a b (b-c)(c-a) + b c (c-a)(a-b) + c a (b-c)(a-b) = (a-b)(b-c)(c-a)+a b(a-b)+b c(b-c)+c a(c-a) (a-b)(b-c)(c-a) =0 array