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**BrianMath** Let $\displaystyle V \subset R^3 $ be the plane defined by the equation $\displaystyle 2x_1 + x_2 =0. Let T:R^3 \rightarrow R^3 $ be the linear transformation defined by reflecting across V. Find the standard matrix for T.

This should be done using change of basis formula. The standard matrix for T, A, should be $\displaystyle A=PBP^{-1} $, where B is the matrix of the transformation with respect to some basis. I chose my basis to be two vectors that are a basis of V and a vector that is in V perp.

How do I find B and solve this problem?