Chapter 5.3, Problem 72E

Consider a vector $\stackrel{\to }{v}$ in ${ℝ}^n$ of theform $\stackrel{\to }{v}=\left[\begin{array}{l}1\\ 1\\ a^2\\ ⋮\\ a^{n-1}\end{array}\right]$ ,where a is any real number. Let P be the matrix ofthe orthogonal projection onto $span\left(\stackrel{\to }{v}\right)$ . Describe the entries of P in terms of a, and explain why P is a Hankel matrix. Sec Exercise 71. As an example, find P for $\stackrel{\to }{v}=\left[\begin{array}{l}1\\ 2\\ 4\end{array}\right]$ .