Question: Let a linear transformation T : R2 R2 be given through two steps: a) reflection in the line y = 2x, and b) rotation by

Let a linear transformation T : R2 R2 be given through two steps: a) reflection in the line y = 2x, and b) rotation by = 3 clockwise. (a) Find the matrices for transformations in each step. (b) Find the matrix of the transformation T . (c) Calculate the image of the point p(2, 3) under this transformation. (d) Calculate the matrix of T1. (e) Calculate the point whose image is the point q(1, 2). (f) What will be the image of the circle of radius 2 centered at p(2, 3) under transformation T and why? (g) What will be the image of the unit circle? (h) What will be the image of the square centered at the origin whose side lengths are =2. (12 marks)

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