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Question:
Determine which of the following transformations are linear transformations.
A. The transformation T defined by T(x1,x2,x3)=(1,×2,x3)
B. The transformation T defined by T(x1,x2)=(2×1−3×2,x1+4,5×2).
C. The transformation T defined by T(x1,x2,x3)=(x1,0,×3)
D. The transformation T defined by T(x1,x2)=(4×1−2×2,3|x2|)
E. The transformation T defined by T(x1,x2,x3)=(x1,x2,−x3)
Answer:
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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