Solve the following problems in python.

Review the concept of a rotation matrix (e.g., p. 60 in the textbook). Show that any matrix of the form (r,s E R) represents a counterclockwise rotation on the plane, preceded or followed by scaling (the scaling factor being nonnegative). Express the angle of rotation and the scaling factor in terms of r and s. In what follows, consider two linear transformations R2 ? R2 with matrices given by A and B. such that and 19 17 (ii) (5 pts) Determine A and B. Verify that both matrices are of the form given in part (1) (iii) (5 pts.) Evaluate the products E-AB and F- BA. Are they equal? Are E and F of the form given in part (i), and if so, what are the corresponding rotation angles and scaling factors? (iv) (5 pts.) Without any further algebra, display a matrix G such that GE = GF = 1 (where I is the 2 x 2 identity matrix) Problem 4B Let 90 h1 In each of the following cases, find matrices P and Q such that PAQ equals the matrix shown. (Note that if either P or Q is not needed, it can be set equal to I.) 0 1 b 0 a d 0 c (iv) l ate 1 b+f d-e+1(x1, .e., a scalar)