Represent each linear map with respect to each pair of bases.
(a) d/dx: Pn → Pn with respect to B, B where B = (1, x, . . . , xn), given by
a0 + a1x + a2x2 + . . . + anxn → a1 + 2a2x + . . . + nanxn-1
(b) ∫: Pn → Pn+1 with respect to Bn, Bn+1 where Bi = (1, x, . . . , xi), given by
a0 + a1x + a2x2 + . . . + anxn → a0x + a1/2x2 + . . . + an / n + 1 xn+1
(c) ∫10: Pn → R with respect to B, ε1 where B = (1, x, . . . , xn) and ε1 = (1), given By
a0 + a1x + a2x2 + . . . + anxn → a0 + a1/2 + . . . + an /n + 1
(d) Eval3: Pn → R with respect to B, ε1 where B = (1, x, . . . , xn) and ε1 = (1), given by
a0 + a1x + a2x2 + . . . + anxn → a0 + a1 ∙ 3 + a2 ∙ 32 + . . . + an ∙ 3n
(e) Slide-1: Pn → Pn with respect to B, B where B = (1, x, . . . , xn), given by
a0 + a1x + a2x2 + . . . + anxn → a0 + a1 ∙ (x + 1) + . . . + an ∙ (x + 1)n