question_answer

If a, b, and c are nonzero real number then \[\Delta =\left| \begin{matrix}    {{b}^{2}}{{c}^{2}} & bc & b+c  \\    {{c}^{2}}{{a}^{2}} & ca & c+a  \\    {{a}^{2}}{{b}^{2}} & ab & a+b  \\ \end{matrix} \right|\]is equal to

A)  abc                 

B)  \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]

C)  bc+ca+ab       

D)  none of these

Correct Answer: D

Solution :

[d] Applying \[{{R}_{1}}\to a{{R}_{1}},\,\,{{R}_{2}}\to b{{R}_{2}}\] and \[{{R}_{3}}\to c{{R}_{3}}\], we get = Applying \[{{C}_{3}}\to {{C}_{3}}+{{C}_{1}}\]and taking \[(bc+ca+ab)\]common, we get [\[\therefore \]\[{{C}_{2}}\]and \[{{C}_{3}}\]are identical]