Exercise 2.5.40

Answers

We have

[\begin{matrix} 1 \\ a & 1 \\ b & 0 & 1 \\ c & 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 \\ 0 & 1 \\ 0 & d & 1 \\ 0 & e & 0 & 1 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ 1 \\ f & 1 \end{matrix}] = [\begin{matrix} 1 \\ a & 1 \\ b & d & 1 \\ c & e & f & 1 \end{matrix}]

In this order, the multipliers $a, b, c, d, e, f$ are unchanged in the product (important for $A = LU$ in Section 2.6).

mathchakra

2021-12-19 17:43