If `x ,y ,z` are different from zero and `"Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0,` then the value of the expression `a/x+b/y+c/z` is a. `0` b. `-1` c. `1` d. `2`

Options

A. 0
B. -1
C. 1
D. 2

Answer

D

Explanation

Applying `R_(2) to R_(2)-R_(1),R_(3) to R_(3) -R_(1)` we get
`Delta = |{:(a,,b-y,,c-z),(-x,,y,,0),(-x,,0,,z:}|=0`
Expanding along `C_(3) ` we get
`" or " (c-z)(xy)+z(ay+bx-xy)=0`
`" or " cxy -xyz +ayz +bxz -xyz =0`
`" or " ayz +bzx + cxz =2xyz`
`" or " (a)/(x)+(b)/(y)+(c )/(z)=2`