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posted by  Duke12 on 4/27/2008 12:56:32 AM  |  status: Live  

Proving linear tranformation

Course Textbook Chapter Problem
Linear Algebra Linear Algebra and Its Applications 3rd by Lay, Stade N/A N/A
Question Details:
Let S: are linear transformations. Show that the mapping is a linear transformation (from )
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posted by gomorycut on 4/27/2008 1:18:48 AM  |  status: Live
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Duke12's comment:
"thanks...studying for finals"
Response Details:
S is linear so S(kx) = kS(x) and S(x+y) = S(x) + S(y)
T is linear so T(kx) = kT(x) and T(x+y) = T(x) + T(y)
 
Now
T(S(kx)) =
= T(kS(x)) (since S is linear)
= kT(S(x)) (since T is linear)
and so scalars, k, can be pulled out of T(S(x))
 
Similarly, T(S(x+y)) =
= T(S(x) + S(y)) (since S is linear)
= T(S(x)) + T(S(y)) (since T is linear)
and so T(S(x)) is a linear transformation.
 
 

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