Exercise 2.3.15

Answers

$a_{ij} = 2 i - 3 j$ :

A = [\begin{matrix} - 1 & - 4 & - 7 \\ 1 & - 2 & - 5 \\ 3 & 0 & - 3 \end{matrix}] \to [\begin{matrix} - 1 & - 4 & - 7 \\ 0 & - 6 & - 12 \\ 0 & - 12 & - 24 \end{matrix}] .

The zero became $- 12$ , an example of fill-in. To remove that $- 12$ , choose

E_{32} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & - 2 & 1 \end{matrix}] .

Every 3 by 3 matrix with entries $a_{ij} = ci + dj$ is singular!

mathchakra

2021-11-20 15:17