Problem 23. Consider the plane P in R³ defined by the equation x+2y+3z = 0 and the line L in R³ spanned 9 by the vector 3 Let S R3 R³ denote the reflection through the plane P: it takes a vector in R³ and 7 • transforms it into its mirror image, the mirror being the plane P. Let T: R3 R³ denote the 90° rotation. → around L of your choice (i.e. you can choose if the rotation is clockwise or counterclockwise). Both S and T are linear transformations (you don't have to prove that). Find the matrix A such that (ToS)(x) = Ax for all vectors R³. Here is some information that you might find useful: The vector 2 is perpendicular to the plane. 3 -21 • The vectors 3 and -7 0 30 are perpendicular to the line. They are also perpendicular to each other.