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Homework Statement
t:P_3 -----> P_3
p(x) |---> p(x) + p(2)
Determine whether or not this function is linear transformation or not.
Homework Equations
For a function to be a linear transformation then t(0) = 0 , there are other axioms that must be satisfied, but that is not the problem.
The Attempt at a Solution
I don't see how this is a linear transformation, since the zero element of P_3 is where p(x) = 0, and t(p(x)) = t(0) = 0 + p (2) ?? surely?
could someone explain why i am totally incorrect please.