Exercise 3.4.5

Answers

(a): $[\begin{matrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{matrix}] \to [\begin{matrix} 1 & 2 & 3 \\ 0 & - 5 & - 7 \\ 0 & - 1 & - 5 \end{matrix}] \to [\begin{matrix} 1 & 2 & 3 \\ 0 & - 5 & - 7 \\ 0 & 0 & - 18 ∕ 5 \end{matrix}] :$
invertible $\Rightarrow$ independent
(b): $[\begin{matrix} 1 & 2 & - 3 \\ - 3 & 1 & 2 \\ 2 & - 3 & 1 \end{matrix}] \to [\begin{matrix} 1 & 2 & - 3 \\ 0 & 7 & - 7 \\ 0 & - 7 & 7 \end{matrix}] \to [\begin{matrix} 1 & 2 & - 3 \\ 0 & 7 & - 7 \\ 0 & 0 & 0 \end{matrix}]; A [\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}]$
add to 0.

mathchakra

2022-01-23 15:42