Let be the plane defined by the equation 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 , 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?
I tried doing this myself where B is and P is where the first two columns of P are a basis of the plane V, and the third column is in V perp, however, my answer did not match the book's answer. Is my choice of P wrong?