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 R3 such that T(v)=-v.
Here's my attempt at the problem:
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.