Chapter 12.4, Problem 3CP

Find the best least squares approximating line for the following vectors, and the projections of the vectors onto the one-dimensional subspace:

$\begin{array}{l}\text{a}\text{. }\left[\begin{array}{c}1\\ 4\end{array}\right],\left[\begin{array}{c}1\\ 5\end{array}\right],\left[\begin{array}{c}2\\ 4\end{array}\right]\\ \text{b}\text{. }\left[\begin{array}{c}2\\ 0\end{array}\right],\left[\begin{array}{c}4\\ 1\end{array}\right],\left[\begin{array}{c}3\\ 2\end{array}\right]\\ \text{c}\text{. }\left[\begin{array}{c}1\\ 2\\ 4\end{array}\right],\left[\begin{array}{c}2\\ 3\\ 5\end{array}\right],\left[\begin{array}{c}2\\ 1\\ 6\end{array}\right],\left[\begin{array}{c}1\\ 1\\ 3\end{array}\right]\end{array}$