I was working on an exercise in which I am given a vector $(2,-1, 2)$ and I am supposed to find the standard matrix $A$ of the reflection operator $T$ on $\mathbb{R}^3$ such that $T(v)=-v$.
Here's my attempt at the problem:
$2x_1-x_2+2x_3=0$
I use it to get $(1,2,0)$ and $(0,-2,1)$ (the two columns of the new matrix $C$) as part of the basis. After that however; I'm confused what I should do. Does anyone have any ideas? I'm not clear so any tips directing me in the right direction would be much appreciated. Thanks.