Exercise 2.5.28

Answers

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

This is $[\begin{matrix} I & A^{- 1} \end{matrix}]$ : row exchanges are certainly allowed in Gauss-Jordan.

mathchakra

2021-12-19 17:36