In the following check to see if the set s is a vector

Question

Q1. In the following check to see if the set S is a vector subspace of the corresponding Rⁿ. If it is not explain why not. If it is, then find a basis and the dimension.

Q2. Use Laplace transforms to solve each problem.

(a) dy/dt + y = f(t),         y(0) = 0, where

(b) d²x/dt² - x = 4t,        x(0) = 3, x'(0) = 1