Question

* Consider the transformations T1=‘reflection across the x-axis’ and T2=‘reflection across the line y = x’. (a) Find the matrices A1 and A2 corresponding to T1 and T2, respectively. (b) Show that (A1) 2 = I, and give a geometrical interpretation of this. (c) Use matrix multiplication to find the geometric effect of T1 followed by T2, showing all your reasoning. (d) The product T (θ)T (φ) of any two reflections T (θ) and T (φ) with angles θ and φ, respectively, is a rotation, with angle c(θ − φ) for some constant c. Based on your results in earlier parts, what can you say about the angle of the rotation, i.e., what is the value of the constant c? Write a MATLAB program to verify your answer for θ = 60◦ and φ =

Answer 1

* Consider the transformations T1=‘reflection across the x-axis’ and T2=‘reflection across the line y = x’. (a) Find the matrices A1 and A2 corresponding to T1 and T2, respectively