Question

$\left|\begin{array}{ccc}1& 1& 1\\ b+c& c+a& a+b\\ b+c-a& c+a-b& a+b-c\end{array}\right|$ is equal to

• A. $abc$
• B. $a+b+c$
• C. $ab+bc+ca$
• D. $0$

Answer 1

The correct option is D $0$

Consider the following question.

$\Delta =\left|\begin{array}{ccc}1& 1& 1\\ b+c& c+a& a+b\\ b+c-a& c+a-b& a+b-c\end{array}\right|$

$c_2\to c_2-c_1{c}_3\to c_3-c_1$

$\left|\begin{array}{cc}a-b& a-b\\ 2(b-c)& 2(b-c)\end{array}\right|=0$

Hence, this is the required answer.