Exercise 2.6.12

Answers

A = [\begin{matrix} 2 & 4 \\ 4 & 11 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 2 & 1 \end{matrix}] [\begin{matrix} 2 & 4 \\ 0 & 3 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 2 & 1 \end{matrix}] [\begin{matrix} 2 & 0 \\ 0 & 3 \end{matrix}] [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}] = LDU;

Note that $U$ is $L^{T}$ . We have

[\begin{matrix} 1 & 4 & 0 \\ 0 & - 4 & 4 \\ 0 & 0 & 4 \end{matrix}] = [\begin{matrix} 1 & 1 \\ 4 & 1 \\ 0 & - 1 & 1 \end{matrix}] [\begin{matrix} 1 & - 4 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}] = LD L^{T} .

mathchakra

2021-12-20 21:06