Question

For positive numbers x, y , z the numerical value of the

determinant

$\left| \begin{matrix} 1 & \log_{x}y & \log_{x}z \\ \log_{y}x & 1 & \log_{y}z \\ \log_{z}x & \log_{z}y & 1 \end{matrix} \right|$is -

• A. 0
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (A)

0

Answer 2

$\left| \begin{matrix} 1 & \frac{\log y}{\log x} & \frac{\log z}{\log x} \\ \frac{\log x}{\log y} & 1 & \frac{\log z}{\log y} \\ \frac{\log x}{\log z} & \frac{\log y}{\log z} & 1 \end{matrix} \right|$

= $\frac { 1 } { \log x \log y \log z }$ $\left| \begin{matrix} \log x & \log y & \log z \\ \log x & \log y & \log z \\ \log x & \log y & \log z \end{matrix} \right|$ = 0