Correct Answer - D
`(d)` The given system of equations will have a non-trivial solution if
`|{:(alpha+a,alpha,alpha),(alpha,alpha+b,alpha),(alpha,alpha,alpha+c):}|=0`
Operate `R_(2)toR_(2)-R_(1)` , `R_(3)-R_(3)-R_(1)`, then
`|{:(alpha+a,alpha,alpha),(-a,b,0),(-a,0,c):}|=0`
`impliesalpha(bc+ca+ab)+abc=0`
Since, `a,b,c ne 0`
`:.(1)/(alpha)=-((1)/(a)+(1)/(b)+(1)/(c ))`