If `x , y , z` are different from zero and `|[1+x,1, 1],[1 , 1+y ,1],[ 1 ,1, 1+z]|=0` then the value of `x^(-1)+y^(-1)+z^(-1)` is (a) `x y z` (b) `x^(-1)y^(-1)z^(-1)` (c) `-x-y-z` (d) `-1`

Explanation

Given , `[[1+x , 1 , 1],[ 1 , 1+y , 1 ],[ 1 , 1 , 1+z]] =0`

`
[[x , -y , 0 ],
[0 , y , -z ],
[1 , 1 , 1+z]]
=0` , use `R_{1} rightarrow R_{1}-R_{2} ` and ` R_{2} rightarrow R_{2}-R_{3}`



Now expand along first row,



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