10 pts (a) Find the standard matrix of the transformation 7 : R- - R' that corresponds to reflection through the line r, -21 = 0 followed by reflection through the line 3.r, -2x1 = 0. Identify the transformation T' (it has a simple geometric description). Hint: the standard matrix for a reflection To through re = ar, is (1 -a") 2a 1 + a2 2a a3 - 1 Finally, identify the transformation T when you reverse the order of the individual reflections. 4 subpts (b) Find the standard matrix of the transformation 7 : R R that corresponds to the anti-clockwise rotation by an angle & about the $1-axis. Check that your matrix has the intended effect of leaving all points on the $1-axis invariant under the rotation. 1 subpts (c) Let 7 : RD - R* be the linear transformation (:1 - 2x2 + 3., + 4x4 - 31,, 1, + 5x, - 3.r; + 714 + 61;. 81 + 11x2 - 3.13 + 2914 + 12.r;)- Write down the standard matrix of this transformation. Prove carefully that T' is neither one-to-one nor onto. 5 subpts