`a ,b ,c`are distinct real numbers not equal to one. If `a x+y+z=0,x+b y+z=0,a n dx+y+c z=0`have nontrivial solution, then the value of `1/(1-a)+1/(1-b)+()/(1-c)`is equal to`1`b. `-1`c.`z e ro`d. none of theseA. `-1`B. `1`C. zeroD. none of these

`a ,b ,c`are distinct real numbers not equal to one. If `a x+y+z=0,x+b

1.	`a ,b ,c`are distinct real numbers not equal to one. If `a x+y+z=0,x+b y+z=0,a n dx+y+c z=0`have nontrivial solution, then the value of `1/(1-a)+1/(1-b)+()/(1-c)`is equal to`1`b. `-1`c.`z e ro`d. none of theseA. `-1`B. `1`C. zeroD. none of these
Answer» Correct Answer - B since the system has non-trivial solution we have `\|{:(a,,1,,1),(1,,b,,1),(1,,1,,c):}\|=0` Applying `R_(1) toR_(1)-R_(2),R_(2) to R_(2) -R_(3) `we get `Delta =\|{:(a-1,,1-b,,0),(0,,b-1,,1-c),(1,,1,,c):}\|=0` `" or " c(1-a)(1-b)+(1-b)(1-c)-(1-c) (a-1)=0` Dividing throughout by (1-a)(1-b)(1-c) we get `(c ) /(1-c) +(1)/(1-a)+(1)/(1-b) =0` `" or " -1 + (1)/(1-c)+(1)/(1-a)+(1)/(1-b)=0` `" or " (1)/(1-c)+(1)/(1-a)+(1)/(1-b) =1`