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)

Question

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)

eva12 · Answer

is it A,D,E that are a linear transformation?

anonymous · Answer

This looks very familiar... Like I just did it today... maybe not, but similar. A is not linear, B is not linear, C is linear, D i believe is non-linear, E is linear. The easiest condition to check is that the zero vector has to map to the zero vector. With A and B, you can plug in a zero vector, and since you add constants, you won't get a zero vector out. Another condition that has to be true is that scalar multiplication must yield the same result, regardless of whether you apply it before or after the transformation. With D, since theres an absolute value, applying a negative scalar would not result in the same transformation as if you multiplied by -1 after the transformation so its non-linear as well. look here if you need any more help: https://en.wikipedia.org/wiki/Linear_map#Algebraic_classifications_of_linear_transformations

eva12 · Answer

Thank you so much=]

anonymous · Answer

Webwork?

eva12 · Answer

yes its webwork

anonymous · Answer

that explains why it looked so familiar haha