# Affine transformation and coordinates of maps

Hi everyone!

I'm having trouble with the following exercise:

Let ##\mathrm {Aff}(ℝ)## be the vector space of the affine maps from ##ℝ## to ##ℝ##:
$$φ_{a,b}:ℝ→ℝ$$ $$x→a x + b$$

Find the contravariant and and covariant coordinate of the map:
$$φ_{1,1}:ℝ→ℝ$$ $$x→x + 1$$ with respect to the bases ##\mathcal{B}:= \left\lbrace 2x,1 \right\rbrace ##

##\mathrm{H}Ψ=\mathrm{E}Ψ##

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