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For one, because you can't transpose lists. Secondly, you should take the (single) entry of c*aa.

aa = vector(var('delta_%d' % i) for i in (0..2))
c = n(matrix(1,3,(-0.5,0.2,.3)),2)
U = e^((c*aa)[0])
show(U)

$$e^{\left(-0.50 \delta_{0} + 0.19 \delta_{1} + 0.25 \delta_{2}\right)}$$

(Note that you specified 2 bits of precision with n.)