If u v and w all positive are the pth qth and rth terms of a GP the determinant of the matrix ........

Mathematics (NDA) Matrices and Determinants

If u, v and w (all positive) are the pth, qth and rth terms of a GP, the determinant of the matrix $\begin{bmatrix} log\; u &p & l\\ log\; v & q &l \\ log\; w & r & l \end{bmatrix}is$

(p – q) (q – r) (r – p)

ln u × ln v × ln w

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Explanation:

$\begin{bmatrix} log\; u &p & l\\ log\; v & q &l \\ log\; w & r & l \end{bmatrix}=0$
( $\because$ u, v, w are in G.P. ⇒ log u, log v, log w are in A.P)