Exercise 2.3.29

Answers

E = [\begin{matrix} 1 & 0 & 0 & 0 \\ - 1 & 1 & 0 & 0 \\ 0 & - 1 & 1 & 0 \\ 0 & 0 & - 1 & 1 \end{matrix}]

subtracts each row from the nextrow. The result

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

still has multipliers $= 1$ in a 3 by 3 Pascal matrix. The product $M$ of all elimination matrices is

[\begin{matrix} 1 & 0 & 0 & 0 \\ - 1 & 1 & 0 & 0 \\ 1 & - 2 & 1 & 0 \\ - 1 & 3 & - 3 & 1 \end{matrix}] .

This "altemating sign Pascal matrix" is on page 91.

mathchakra

2021-11-20 15:24