Chapter 4.1, Problem 1CP

Form the normal equations, and compute the least squares solution and 2-norm error for the following inconsistent systems:

$\text{a}.\left[\begin{array}{l}\begin{array}{ccc}3& -1& 2\end{array}\\ \begin{array}{ccc}4& 1& 0\end{array}\\ \begin{array}{ccc}-3& 2& 1\end{array}\\ \begin{array}{ccc}1& 1& 5\end{array}\\ \begin{array}{ccc}-2& 0& 3\end{array}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}10\\ 10\\ -5\\ \begin{array}{l}15\\ 0\end{array}\end{array}\right]$

$\text{b}.\left[\begin{array}{l}\begin{array}{cccc}4& 2& 3& 0\end{array}\\ \begin{array}{cccc}-2& 3& -1& 1\end{array}\\ \begin{array}{cccc}1& 3& -1& 2\end{array}\\ \begin{array}{cccc}1& 0& 1& -1\end{array}\\ \begin{array}{cccc}3& 1& 3& -1\end{array}\end{array}\right]\left[\begin{array}{l}\begin{array}{c}{x}_1\\ x_2\end{array}\\ \begin{array}{c}{x}_3\\ x_4\end{array}\end{array}\right]=\left[\begin{array}{c}10\\ 0\\ 2\\ \begin{array}{l}0\\ 5\end{array}\end{array}\right]$