which of the following transformations are linear Which of t

Which of the following transformations are linear?

Solution

Linear transforms have to fulfill 2 axioms: for any vectors v and w,

T(v + w) = Tv + Tw (transforms are additive);
T(a*v) = a*Tv for some scalar a (transforms are scalar multiplicative).

So test against these.

we get A, C, D ae linear