Exercise 2.6.2

Answers

$L c = b$ is

[\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix}] [\begin{matrix} c_{1} \\ c_{2} \end{matrix}] = [\begin{matrix} 5 \\ 7 \end{matrix}],

solved by $c = [\begin{matrix} 5 \\ 2 \end{matrix}]$ as elimination goes forward.

$U x = c$ is

[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5 \\ 2 \end{matrix}],

solved by $x = [\begin{matrix} 3 \\ 2 \end{matrix}]$ in back substitution.

mathchakra

2021-12-20 20:49