(Reflection matrix) Let u be a unit vector in R". Define an n X n matrix A = I - 2uuh. (a) Verify by definition that A is an orthogonal matrix. (b) Verify that A2 = I. (c) What is AT if a is orthogonal to u? (d) Verify that the map fA : R" - R" associ- ated to A is the reflection across the subspace orthogonal to u. Hint: Note that Ax = x -2uu' x, and uu r is exactly the projection of x onto the u direction, so a decomposes as a = uu a + ( - uud), and the second part is the part orthogonal to u. Now AT = (x - uulx) - uut. It would be clearer if you draw a picture