Chapter 3, Problem 9SE

Exercise 9 and 10 concern determinants of the following vander-monde matrices.

$T=\left[\begin{array}{ccc}1& a& a^2\\ 1& b& b^2\\ 1& c& c^2\end{array}\right],V(t)=\left[\begin{array}{cccc}1& t& t^2& t^3\\ 1& x_1& x_1^2& x_1^3\\ 1& x_2& x_2^2& x_2^3\\ 1& x_3& x_3^2& x_3^3\end{array}\right]$

9. Use row operations to show that

det T = (b − a)(c − a)(c − b)