The determinant | array lll b _ 1 + c _ 1 & c _ 1 + a _ 1 & a _ 1 + b _ 1 ~b _ 2 + c _ 2…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
The determinant \[\left|\begin{array}{lll}
\mathrm{b}_{1}+\mathrm{c}_{1} & \mathrm{c}_{1}+\mathrm{a}_{1} & \mathrm{a}_{1}+\mathrm{b}_{1} \\
\mathrm{~b}_{2}+\mathrm{c}_{2} & \mathrm{c}_{2}+\mathrm{a}_{2} & \mathrm{a}_{2}+\mathrm{b}_{2} \\
\mathrm{~b}_{3}+\mathrm{c}_{3} & \mathrm{c}_{3}+\mathrm{a}_{3} & \mathrm{a}_{3}+\mathrm{b}_{3}
\end{array}\right|=\]
- \[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\]
- 2\[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\]
- 3\[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\]
- none of these
Answer
(B) 2 | array lll a _ 1 & ~b _ 1 & c _ 1 a _ 2 & ~b _ 2 & c _ 2 a _ 3 & ~b _ 3 & c _ 3 array |
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