I'm a bit confused about rotation and reflection matrices

[PirateFan308]

Homework Statement

I have a final coming up and I am a bit fuzzy on how to create a matrix that represents a rotation or reflection about a certain plane (in R3). Say we are given a rotation/reflection about either a plane or a line through two points T(v)=Av and we are told to find A. Do we simply have to look at $e_1, e_2, e_3$ and see what the transition would be for these vectors and plug the 'transitioned' $e_1, e_2, e_3$ into the columns of A, respectively? Or is there a lot more that I am missing? Thanks!

 

[vela]

Yup, that's how you find the columns of the matrix representing any linear transformation.