Determine which of the following transformations are linear transformations.

AThe transformation T defined by T(x1,x2,x3)=(1,x2,x3)
BThe transformation T defined by T(x1,x2)=(2x1−3x2,x1+4,5x2).
CThe transformation T defined by T(x1,x2,x3)=(x1,0,x3)
DThe transformation T defined by T(x1,x2)=(4x1−2x2,3|x2|)
EThe 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 · 2022-03-03T06:04:37-05:00

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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