4. Consider the linear transformation Qm: R² → R² that reflects a vector over the line y = mx. [H]. Show that the matrix for the linear transformation T(T) = proj() is (a) Let u = given by (b) Now use the diagram below (and the fact that the diagonals of a parallelogram bisect each other) to show that Qm() = 2proj(x) - T. Y 1 A = uu¹ ||ū||² Qm (x) proj() (c) Use parts (a) and (b) to show that the matrix for Qm is [1 - m² - 2m 1+m² 1+m² 2m 1+m² (d) Show that (QmQm)(x) = for all in R². m² - 1 1+ m² X

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