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)

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.

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andromache andromache · Answer 2 · 2022-03-03T12:04:37+01:00

The transformations are linear transformations should be option C and option E.

Linear transformation:

With respect to A and B, it looks like a linear transformation, but when the constants are added so it will not zero out. For the letter D, it is not a linear transformation because of the scalar multiplication. The value given in D should contain an absolute value so there is no effect.

Therefore, The transformations are linear transformations should be option C and option E.

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