Determine the following:
(a) dim span(f1, f2, f3, f4) ? r5[x] where
f1 = 2x + x 3 ? x 4 , f2 = 1 + x + x 5 , f3 = 1 + 3x + 2x 2 + x 3 ? 2x 5 , f4 = 2x 2 + x 4 ? 3x 5
(b) dim v ? m3×2(r) where
v = {m(w, x, y, z) : m(w, x, y, z) =
(w + x + 2y + z ? w + x ? 2y ? z)
(2w ? 2x + 4y ? z ? 2w + x ? 4y + 2z)
(w ? x + 2y + 2z w + 2x + 2y ? 2z ) ; w, x, y, z ? r}.