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)

The answer is letter C and E.

For A and B, they look like a linear transformation, however when you add the constants, it will not zero out. For letter D, it is not a linear transformation because of the scalar multiplication. The value given in D is an absolute value, so whether or not you multiply this, it will not result to the same number.

1     sepan

2     encuentren

3     tenga

4     hable

5   parezca

6   llegue

it's