Question

Need help solving this determinant

Answer 1

If \(\Large a_i b_j \neq 1\) & \(\LARGE a_1<a_2<a_3\) & \(\LARGE b_1<b_2<b_3\),Then:
\[ \left| \begin{array}{ccc} \frac{1-a_1 ^3 b_1 ^3}{1-a_1 b_1} & \frac{1-a_1 ^3 b_2 ^3}{1-a_1 b2} & \frac{1-a_1 ^3 b_3 ^3}{1-a_1 b_3}\\ \frac{1-a_2 ^3 b_1 ^3}{1-a_2 b_1} & \frac{1-a_2 ^3 b_2 ^3}{1-a_2 b_2} & \frac{1-a_2 ^3 b_3 ^3}{1-a_2 b_3} \\ \frac{1-a_3 ^3 b_1 ^3}{1-a_3 b_1} & \frac{1-a_3 ^3 b_2 ^3}{1-a_3 b_2} & \frac{1-a_3 ^3 b_3 ^3}{1-a_3 b_3} \end{array} \right|.\]
is
(i)Positive(+ve)
(ii)Non Positive(+ve)
(iii)Negative
(iv) Non negative

Answer 2

@oldrin.bataku @zepdrix @Jonask @terenzreignz

Answer 3

\[\Huge\left| \begin{array}{ccc} \frac{1-a_1 ^3 b_1 ^3}{1-a_1 b_1} & \frac{1-a_1 ^3 b_2 ^3}{1-a_1 b2} & \frac{1-a_1 ^3 b_3 ^3}{1-a_1 b_3}\\ \frac{1-a_2 ^3 b_1 ^3}{1-a_2 b_1} & \frac{1-a_2 ^3 b_2 ^3}{1-a_2 b_2} & \frac{1-a_2 ^3 b_3 ^3}{1-a_2 b_3} \\ \frac{1-a_3 ^3 b_1 ^3}{1-a_3 b_1} & \frac{1-a_3 ^3 b_2 ^3}{1-a_3 b_2} & \frac{1-a_3 ^3 b_3 ^3}{1-a_3 b_3} \end{array} \right|.\]
Bigger version :P