Determine which of the following transformations are linear transformations
A. The transformation $T_1$ defined by $T_1(x_1,x_2,x_3)=(x_1,0,x_3)$
B. The transformation $T_2$ defined by $T_2(x_1,x_2)=(2x_1−3x_2,x_1+4,5x_2)$.
C. The transformation $T_3$ defined by $T_3(x_1,x_2,x3)=(x_1,x_2,−x_3)$
D. The transformation $T_4$ defined by $T_4(x_1,x_2,x3)=(1,x_2,x_3)$
E. The transformation $T_5$ defined by $T_5(x_1,x_2)=(4x_1−2x_2,3|x_2|)$.
I believe that it could be A and E. How can I determine this? If someone could show me one I could figure out the rest.