Question

For positive numbers x, y, z, the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` is

विकल्प

• 0

• 1

• 2

• None of these

Answer 1

0

Explanation:

We have, `|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)| = |(1, logy/logx, logz/logx),(logx/logy, 1, log z/logy),(logx/logz, logy/logz, 1)|`

= `1/(log x. log y. log z) |(log x, log y, log z),(log x, log y, log z),(log x, log y, logz)|`   .....[∵ All rows are identical]

= 0