For each of the following linear transformations of

R2, determine the 2 × 2 matrix representing that transformation (simplify your matrix entries as much as possible):

(i) a reflection in the x-axis;

(ii) a rotation about the origin through a counterclockwise angle of Pie/2;

(iii) the transformation made by performing a reflection in the x-axis followed by

a rotation about the origin through a counterclockwise angle of Pie/2;

(iv) the transformation made by performing a rotation about the origin through

a counterclockwise angle of Pie/2 followed by a reflection in the x-axis.