A) \[\frac{462{{a}^{5}}}{{{b}^{6}}}\]
B) \[-\frac{462{{a}^{5}}}{{{b}^{6}}}\]
C) \[-\frac{462{{a}^{6}}}{{{b}^{5}}}\]
D) 0
Correct Answer: D
Solution :
\[\left| \begin{matrix} a+b & a+2b & a+3b \\ a+2b & a+3b & a+4b \\ a+4b & a+5b & a+6b \\ \end{matrix} \right|\] \[{{R}_{2}}\to {{R}_{2}}-{{R}_{1}}\] \[{{R}_{3}}\to {{R}_{3}}-{{R}_{2}}\] \[\left| \begin{matrix} a+b & a+2b & a+3b \\ b & b & b \\ 2b & 2b & 2b \\ \end{matrix} \right|=0\](\[\because \]two rows are identical)
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