If a, b, c are positive and unequal, show that value of the determinant `Delta=|(a,b,c),(b,c,a),(c,a,b)|` is negative

Answer

Proved

Explanation

`R_{1} \rightarrow R_{1}+R_{2}+R_{3}` is
$$\Delta=\left|\begin{array}{ccc}a+b+c & a+b+c & a+b+c \\ b & c & a \\ c & a & b\end{array}\right|$$
$$
\begin{aligned}
&\Rightarrow \Delta=(a+b \\
&=\left|\begin{array}{lll}
1 & 1 & 1 \\
b & c & a \\
...