Are the following sets vector spaces? Explain why or why not a) The set of continuous...

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Are the following sets vector spaces? Explain why or why not a) The set of continuous functions f from R to R for which fof(t)dt = 0 b) Fix a positive integer n. Consider the set, Pn(R) of all polynomials of degree ≤n with coefficients from Rin the Independent z.Algebraically, P₁ (R)=(ao+az + a₂z²+.... +aza ER,0 ≤i≤n). Are the following sets vector spaces? Explain why or why not a) The set of continuous functions f from R to R for which fof(t)dt = 0 b) Fix a positive integer n. Consider the set, Pn(R) of all polynomials of degree ≤n with coefficients from Rin the Independent z.Algebraically, P₁ (R)=(ao+az + a₂z²+.... +aza ER,0 ≤i≤n).