MCQ
The determinant $\left| {\begin{array}{*{20}{c}}{{b_1}\, + \,\,{c_1}}&{{c_1}\, + \,\,{a_1}}&{{a_1}\, + \,\,{b_1}}\\{{b_2}\, + \,\,{c_2}}&{{c_2}\, + \,\,{a_2}}&{{a_2}\, + \,\,{b_2}}\\{{b_3}\, + \,\,{c_3}}&{{c_3}\, + \,\,{a_3}}&{{a_3}\, + \,\,{b_3}} \end{array}} \right|$ $=$
  • A
    $\left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$
  • $2$ $\left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$
  • C
    $3$ $\left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$
  • D
    $4$ $\left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$

Answer

Correct option: B.
$2$ $\left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$
b
$C_1 \rightarrow C_1 + C_2 + C_3$

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