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Question Number 214447 by 2universe456 last updated on 08/Dec/24

Commented by Frix last updated on 08/Dec/24

$$=abc$$

Answered by Rasheed.Sindhi last updated on 09/Dec/24

$$\left|\begin{array}{cccc}1& 1& 1& 1\\ 1& a+1& 1& 1\\ 1& 1& 1+b& 1\\ 1& 1& 1& 1+c\end{array}\right|$$$$Subtract{\mathrm{C}}_{1}from{\mathrm{C}}_2,{\mathrm{C}}_3\mathrm{\&}{\mathrm{C}}_4$$$$=\left|\begin{array}{cccc}1& 0& 0& 0\\ 1& a& 0& 0\\ 1& 0& b& 0\\ 1& 0& 0& c\end{array}\right|$$$$=\left|\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right|$$$$=a\left|\begin{array}{cc}b& 0\\ 0& c\end{array}\right|$$$$=a(bc-0)=abc$$

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