Question

The value of the determinant ∆= $\left| \begin{matrix} \log x & \log y & \log z \\ \log 2x & \log 2y & \log 2z \\ \log 3x & \log 3y & \log 3z \end{matrix} \right|$ is –

• A. 0
• B. log (xyz)
• C. log (6xyz)
• D. 6 log(xyz)

Answer 1

Answer: (A)

0

Answer 2

∆= $\left| \mspace{6mu}\begin{matrix} \log x & \log y & \log z \\ \log 2 + \log x & \log 2 + \log y & \log 2 + \log z \\ \log 3 + \log x & \log 3 + \log y & \log 3 + \log z \end{matrix}\mspace{6mu} \right|$ R₂ → R₂ – R₁ ,

R₃ → R₃ – R₁

∆ = $\left| \mspace{6mu}\begin{matrix} \log x & \log y & \log z \\ \log 2 & \log 2 & \log 2 \\ \log 3 & \log 3 & \log 3 \end{matrix}\mspace{6mu} \right|$

= (log 2) (log3) $\left| \mspace{6mu}\begin{matrix} \log x & \log y & \log z \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}\mspace{6mu} \right|$ = 0