Exercise 2.5.41

Answers

4 by 4 still with $T_{11} = 1$ has pivots $1, 1, 1, 1$ ; reversing to $T^{∗} = UL$ makes $T_{44}^{∗} = 1$ .

T = [\begin{matrix} 1 & - 1 & 0 & 0 \\ - 1 & 2 & - 1 & 0 \\ 0 & - 1 & 2 & - 1 \\ 0 & 0 & - 1 & 2 \end{matrix}] and T^{- 1} = [\begin{matrix} 4 & 3 & 2 & 1 \\ 3 & 3 & 2 & 1 \\ 2 & 2 & 2 & 1 \\ 1 & 1 & 1 & 1 \end{matrix}]

mathchakra

2021-12-19 17:43