Question

Verify that T2 x T1 is a linear transfromation when T1: U->V and T2: V->W

Answer 1

Both T1 and T2 are linear transformations

Answer 2

T2 x T1 means the composition of them i presume

Answer 3

Yes, it can also be written T2T1

Answer 4

then just check the two conditions for a mapping to be linear transformation

Answer 5

T2T1(ax + y)
= T2[a(T1)(x) +(T1)(y)] by the linearity of T1
=T2[a(T1)(x)] + (T2)(T1)y by the linearity of T2
=aT2T1(x) + T2T1(y)