Question

The value of the determinant $\left|\begin{array}{ccc}1& a& b+c\\ 1& b& c+a\\ 1& c& a+b\end{array}\right|$ is

• A. a+b+c
• B. $(a+b+c{)}^2$
• C. 1+a+b+c

Answer 1

$\Delta =\left|\begin{array}{ccc}1& a& b+c\\ 1& b& c+a\\ 1& c& a+b\end{array}\right|=(a+b+c)\left|\begin{array}{ccc}1& 1& b+c\\ 1& 1& c+a\\ 1& 1& a+b\end{array}\right|(C_2\to C_2+C_3)=0,(\because C_1\equiv C_2)$.