4) (10 points) The following are subsets of R³:
Wi = {(aâ‚, aâ‚‚, a₃) ∈ R³ | aâ‚ + aâ‚‚ + a₃ = 0}
Wz = {(aâ‚, aâ‚‚, a₃) ∈ R³ | aâ‚ + 4aâ‚‚ + a₃ = 0}
W3 = {(aâ‚, aâ‚‚, a₃) ∈ R³ | aâ‚ + 2aâ‚‚ + 3a₃ = 0}
a) Give a vector description of each set.
b) Describe Wi ∩ Wz, Wi ∩ W3, and Wz ∩ W3.
c) Are the intersections in (b) a subspace of R³?