Chapter 5, Problem 12CTB

(a)

To determine

To show that $u_1\left(x\right)=\frac{1}{\sqrt{2}}\text{ and }{u}_2\left(x\right)=\frac{\sqrt{6}}{2}x$ form an orthonormal set of vectors.

(b)

To determine

To find the best least squares approximation to $h\left(x\right)=x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+x^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ by a linear function.