Exercise 2.7.9

Answers

We have

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

but

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

If $P_{3}$ and $P_{4}$ exchange different pairs of rows, $P_{3} P_{4} = P_{4} P_{3} =$ both exchanges.

mathchakra

2022-01-16 12:15