Exercise 2.6.16

$\left[\begin{array}{ccc}1\hfill & 0\hfill & 0\hfill \\ 1\hfill & 1\hfill & 0\hfill \\ 1\hfill & 1\hfill & 1\hfill \end{array}\right]c=\left[\begin{array}{c}4\hfill \\ 5\hfill \\ 6\hfill \end{array}\right]$gives $c=\left[\begin{array}{c}4\hfill \\ 1\hfill \\ 1\hfill \end{array}\right].$Then $\left[\begin{array}{ccc}1\hfill & 1\hfill & 1\hfill \\ 0\hfill & 1\hfill & 1\hfill \\ 0\hfill & 0\hfill & 1\hfill \end{array}\right]x=\left[\begin{array}{c}4\hfill \\ 1\hfill \\ 1\hfill \end{array}\right]$gives $x=\left[\begin{array}{c}3\hfill \\ 0\hfill \\ 1\hfill \end{array}\right]$. Those are forward elimination and back substitution for $\left[\begin{array}{ccc}1\hfill & 1\hfill & 1\hfill \\ 1\hfill & 2\hfill & 2\hfill \\ 1\hfill & 2\hfill & 3\hfill \end{array}\right]x=\left[\begin{array}{c}4\hfill \\ 5\hfill \\ 6\hfill \end{array}\right].$