anonymous
  • anonymous
Verify that T2 x T1 is a linear transfromation when T1: U->V and T2: V->W
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Both T1 and T2 are linear transformations
anonymous
  • anonymous
T2 x T1 means the composition of them i presume
anonymous
  • anonymous
Yes, it can also be written T2T1

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

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