Linear Transformation of s u + r V

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SUMMARY

The discussion centers on the definition and properties of linear transformations, specifically focusing on the expression T(su + rV), where s and r are scalars and u and v are vectors. It is established that T(su + rV) = sT(u) + rT(v) confirms the linearity of the transformation T. Additionally, the composition of two linear transformations, S(T), is confirmed to also be a linear transformation, provided T maps from vector space U to V and S maps from V to W.

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hi,

Could someone please show me how these are a linear transformation please:

1) T(s u + r V)
s and r are scalars and u and v are vectors.

2) composite function:
u : v

thanks
 
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that would depend on what T is, and what : means, 'composite function' not being something standard, at least not in any useful sense here.
 
The questions as stated make no sense.

T(su+ rv)= sT(u)+ rT(v) is the definition of "linear transformation".

If you have one linear transformation T from, say, vector space U to vector space V, and another linear transformation S from V to vector space W, then it is true that
the composition S(T), from U to W, is a linear transformation. Is that what you mean?
 

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