Let T : R 3 → R 3 be the linear transformation corresponding to rotating by π/4 clockwise around the z-axis, and then reflecting over the x-axis. Since T is a linear transformation, it corresponds to left multiplication by some matrix A.
I am familiar with linear transformation problems that give you specific vectors, but this one doesn't. I know I have to use the standard basis vectors to determine the transformed vectors which make up the final matrix. I just don't know how to go about doing that though. Thanks