Find the standard matrix for F: R3 to R3, the reflection across the plane H= {x | 2x+y+z=0}.

[lreyes]

Find the standard matrix for F: R3 to R3, the reflection across the plane H= {x | 2x+y+z=0}.

I have this problem for my Linear Algebra class and I am not sure how to move forward with the calculations. I am able to do similar problems in R2 but am having trouble in R3.

So far I have been using the formulas:
[T]B = [[T(b1)]B | [T(b2)]B] (B-matrix for T)
[T] = B * [T]B * B^-1 (Standard matrix for T)

Could somebody, please, help me with this problem? Thank you. ?

 

[Steven G]

You are given the steps. Can you do the 1st step? Can we please see your work?