Determine which of the following transformations are linear transformations.

a. the transformation t defined by t(x1,x2,x3)=(1,x2,x3)
b. the transformation t defined by t(x1,x2)=(2x1−3x2,x1+4,5x2).
c. the transformation t defined by t(x1,x2,x3)=(x1,0,x3)
d. the transformation t defined by t(x1,x2)=(4x1−2x2,3|x2|)
e. the transformation t defined by t(x1,x2,x3)=(x1,x2,−x3)