1) Let T₁ and T₂ be reflections in lines y = 0 and y = x respectively. Which of the following linear transformations is equal to T₁ T₂? circle the correct answer. (you are not required to justify your answer)

(a) Reflection in line x = 0. (b) Reflection in line y = (1/2)X (c) Counterclockwise rotation about the origin through an angle of /2.

(d) Counterclockwise rotation about the origin through an angle of /4. (e) Clockwise rotation about the origin through an angle of/2.

(f) Clockwise rotation about the origin through an angle of /4. (g) Other (specify).

2) Let T be a liner transformation such that T [1 1 0 -1]^T = [2 3 -1]^T and T [0 -1 1 1]^T = [5 0 1]^T. Find T [1 3 -2 -3]^T?

3) Determine whether the following transformation T : R² R³ is a linear transformation. Clearly state your answer. If it is a liner transformation, express it as a matrix transformation.

a) T [X Y]^T = [2Y X X-3Y]^T (b) T [X Y]^T = [X-Y X Y-1]^T (c) T [X Y]^T = [X+Y XY X]^T (d) T [x y]^T = [x y 0(zero)]^T + [1 1 1]^T

4) Let A= [2 3 -3] [1 0 -1] [1 1 -2] and B= [0 1 0] [3 0 1] [2 0 0]. Show that C_A(x)= C_B(x)= (x+1)² (x2), but A is diagonalizable and B is not.