Question: How to prove one function is linear transformation by maple

 Today I read the  Problem 5.21 from book Maple and Mathematica, A Problem Solving Approach for Mathematics:

The book uses following codes:

with(LinearAlgebra): n:=9; v:=Vector(n); T:=v->add(v[i]*x^(i-1),i=1..n); P:=Vector(n,symbol=p); Q:=Vector(n,symbol=q); Z1:=T(a*P+b*Q); Z2:=a*T(P)+b*T(Q);

But I think  these codes just verify rather than prove(n is always specific number). This example is not difficult to prove by hand. but I'd like to know Maple how to prove it. It seems not easy.












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