A) \[(ab-{a}'{b}')(bc-{b}'{c}')(ca-{c}'{a}')\]
B) \[(ab+{a}'{b}')(bc+{b}'{c}')(ca+{c}'{a}')\]
C) \[(a{b}'-{a}'b)(b{c}'-{b}'c)(c{a}'-{c}'a)\]
D) \[(a{b}'+{a}'b)(b{c}'+{b}'c)(c{a}'+{c}'a)\]
Correct Answer: C
Solution :
Trick: Put \[a=1,\,b=-1,\,c=0\] \[{a}'=2,\,{b}'=2,\,{c}'=1\] Then the determinant is \[\left| \,\begin{matrix} 0 & -1 & 2 \\ 0 & 1 & 2 \\ -1 & 0 & 4 \\ \end{matrix}\, \right|=4\] Option (c) also gives the same value.You need to login to perform this action.
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