Chapter 10, Problem 17P

Besides the Hilbert matrix, there are other matrices that are inherently ill-conditioned. One such case is the Vandermonde matrix, which has the following form:

$\left[\begin{array}{ccc}{x}_1^2& x_1& 1\\ x_2^2& x_2& 1\\ x_3^2& x_3& 1\end{array}\right]$

(a) Determine the condition number based on the row-sum norm for the case where $x_1=4,x_2=2,\text{ and }{x}_3=7$.

(b) Use MATLAB or Mathcad software to compute the spectral and Frobenius condition numbers.