(a) write down the linear transformation in r 2 (with domain and codomain) that reflects a vector about the y-axis. call the associated matrix a. (b) write down the linear transformation in r 2 (with domain and codomain) that rotates a vector counterclockwise by 180 degrees. call the associated matrix b. (c) write down the linear transformation in (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). write the matrix explicitly. (d) write down the matrix of the linear transformation that first rotates as in (b), then reflects as in (a), and then rotates backwards (that is, clockwise by 180 degrees). write the matrix explicitly. (e) what matrix do you get if you repeat the sequence in part (d) k times? write the matrix explicitly.