Question: a) This part is about mirror reection transformations in two dimensions: i) Find the matrix M that performs a mirror-reflection of two- dimensional vectors, with

a) This part is about mirror reection transformations in two dimensions: i) Find the matrix M that performs a mirror-reflection of two- dimensional vectors, with a mirror symmetry line given by the equation y = mx with m an arbitrary slope. Hint: The answer is M = 1 (1 m2 2m 1+m2 2m m2 1 use the answer in your derivation. You must derive it. ) but you may not [5 marks] ii) Calculate the determinant det(M) and calculate the inverse matrix M'l. Explain your results in terms of the linear transformation that M represents. [2 mark] iii) Calculate (or use a reasoned argument to find) all the eigenvalues of this matrix. [2 marks]

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