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. In this question we will investigate a linear transformation F : R 2 → R...

. In this question we will investigate a linear transformation F : R 2 → R 2 which is defined by reflection in the line y = 2x. We will find a standard matrix for this transformation by utilising compositions of simpler linear transformations. Let Hx be the linear transformation which reflects in the x axis, let Hy be reflection in the y axis and let Rθ be (anticlockwise) rotation through an angle of θ. (a) Explain why F = Rθ ◦ Hx ◦ R−θ for an appropriate choice of θ, and use this to calculate the standard matrix of F.

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