questions below:

Assume that T is a linear transformation. Find the standard matrix of T. T: R2 - R2 first rotates points through 6 radians and then reflects points through the horizontal x, -axis. . . . A= (Type an integer or simplified fraction for each matrix element. Type exact answers, using radicals as needed.)For the subspace below, (a) nd a basis for the subspace, and (b) state the dimension. p-6q 6p+2r _ :p,q,r|nR -6q+3r -3p+6r (a) Find a basis for the subspace. A basis for the subspace is D. (Use a comma to separate answers as needed.) (b) State the dimension. The dimension is D. Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations shown below. X1 + 2X2 - 3X3 = - 4 X1 + 2X2 -3X3 = 0 x 1 2x1 + X2 - 3X3 = -5 2x1 + X2 -3X3 =0 where the solution set is x = |X2 - X1 + X2 = 1 - X1 + X2 = 0 . . . Describe the solution set of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.) O A. X= OB. X=X2 OC. X= +X3 OD. X=X2 +X3 Which option best compares the two systems? O A. The solution set of the first system is a line parallel to the line that is the solution set of the second system. O B. The solution set of the first system is a line perpendicular to the line that is the solution set of the second system. O C. The solution set of the first system is a plane parallel to the line that is the solution set of the second system. O D. The solution set of the first system is a plane parallel to the plane that is the solution set of the second system