Exercise 2.6.7

Answers

E_{32} E_{31} E_{21} A = [\begin{matrix} 1 \\ 1 \\ - 2 & 1 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ - 3 & 1 \end{matrix}] [\begin{matrix} 1 \\ - 2 & 1 \\ 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 2 & 2 & 2 \\ 3 & 4 & 5 \end{matrix}] .

This is

[\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{matrix}] = U .

Put those multipliers $2, 3, 2$ into $L$ . Then

A = [\begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{matrix}] U = LU .

mathchakra

2021-12-20 21:01