A) \[\left| \begin{matrix} bx+ay & cx+by \\ b'x+a'y & c'x+b'y \\ \end{matrix} \right|\]
B) \[\left| \begin{matrix} ax+by & bx+cy \\ a'x+b'y & b'x+c'y \\ \end{matrix} \right|\]
C) \[\left| \begin{matrix} bx+cy & ax+by \\ b'x+c'y & a'x+b'y \\ \end{matrix} \right|\]
D) \[\left| \begin{matrix} ax+by & bx+cy \\ a'x+b'y & b'x+c'y \\ \end{matrix} \right|\]
Correct Answer: D
Solution :
[d] \[\text{Let}\,\Delta =\left| \begin{matrix} {{y}^{2}} & -xy & {{x}^{2}} \\ a & b & c \\ a' & b' & c' \\ \end{matrix} \right|\] Then, [Applying\[{{C}_{1}}\to x{{C}_{1}},{{C}_{3}}\to y{{C}_{3}}\]] [Applying\[{{C}_{1}}\to {{C}_{1}}+y{{C}_{2}},{{C}_{3}}\to {{C}_{3}}+x{{C}_{2}}\]] [Expanding along\[{{R}_{1}}\]]You need to login to perform this action.
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