Question

The value of the determinant $\left(\begin{array}{ccc}\log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{array}\right|$ is .

• A. log x +log y +log z
• B. log x log y log z
• C. 0.0
• D. 1

Answer 1

The correct option is C 0.0

$\Delta =\left(\begin{array}{ccc}\log x& \log y& \log z\\ \log 2+\log x& \log 2+\log y& \log 2+\log z\\ \log 3+\log x& \log 3+\log y& \log 3+\log z\end{array}\right|\mathrm{On}\mathrm{applying}{R}_3\to R_3-R_1,R_2\to R_2-R_1,\mathrm{we}\mathrm{get}-\left(\begin{array}{ccc}\log x& \log y& \log z\\ \log 2& \log 2& \log 2\\ \log 3& \log 3& \log 3\end{array}\right|=\left(\log 2\right)\left(\log 3\right)\left(\begin{array}{ccc}\log x& \log y& \log z\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|=0$