A) The arithmetic mean of a and b
B) The geometric mean of a and b
C) The harmonic mean of a and b
D) Equal to zero
Correct Answer: B
Solution :
\[\,\left| \,\begin{matrix} a & a & c \\ 1 & 0 & 1 \\ c & c & b \\ \end{matrix}\, \right|=0\Rightarrow \left| \,\begin{matrix} a & 0 & c \\ 1 & -1 & 1 \\ c & 0 & b \\ \end{matrix}\, \right|=0\] {Applying \[{{C}_{2}}\to {{C}_{2}}-{{C}_{1}}\}\] \[\Rightarrow a\,(-b)+c\,(c)=0\Rightarrow {{c}^{2}}=ab.\] Hence \[c\] is the geometric mean of \[a\] and \[b.\]You need to login to perform this action.
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