A) \[2A+B=0\]
B) \[2A-B=0\]
C) \[A+2B=0\]
D) \[A-2B=0\]
Correct Answer: B
Solution :
| \[B=2.2\,\,\left| \begin{matrix} f & d & e \\ n & \ell & m \\ c & a & b \\ \end{matrix} \right|\] |
| [Taking 2 common from \[{{R}_{2}}\] and \[{{C}_{2}}\]] |
| \[=2\,\,\left| \begin{matrix} 2f & d & e \\ 2n & \ell & m \\ 2c & a & b \\ \end{matrix} \right|\] \[=2\,\,\left| \begin{matrix} 2c & a & b \\ 2f & d & e \\ 2n & \ell & m \\ \end{matrix} \right|\] |
| [\[{{R}_{3}}\leftrightarrow {{R}_{2}},\] then \[{{R}_{2}}\leftrightarrow {{R}_{1}}\]] |
| \[=2\,\,\left| \begin{matrix} a & b & 2c \\ d & e & 2f \\ \ell & m & 2n \\ \end{matrix} \right|=2A\] |
| [\[{{C}_{1}}\leftrightarrow {{C}_{2}}\] and \[{{C}_{2}}\leftrightarrow {{C}_{3}}\]] |
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