Prove that :`Det[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)`

1.	Prove that :`Det[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)`
Answer» LHS= `\|(1+a, 1,1),(1, 1+b, 1),(1,1,1+c)\|` `R_1-> R_1-(1+a)R_3` `R_2-> R_2 - R_3` `\|(0,-a,1-(1+c)(1+a)),(0,b,-c),(1,1,1+c)\|` `= \|(0,-a,-c-a+ac),(0,b,-c),(1,1,1+c)\|` expand `c_1` `= 0+0+1\|(-a,-c-a+ac),(b,-c)\| ` `= ac -[(b)(-c-a-ac)]` `= ac +bc +ba + abc` `= abc(1/b +1/a +1/c+1)` Answer

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Prove that :`Det[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)`

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