(a) Let V be a vector space, let v1, V2, V3, V4 E V, and suppose that v4 is a linear combination of v1, v2, v3. Show that Span(V1, . . ., V4) = Span(V1, V2, V3). Take care to show that every vector in Span(V1, V2, V3) is in Span(V1, . .., V4) and conversely that every vector in Span(V1, . . ., V4) is in Span(V1, V2, V3). (b) Let W be the vector space of functions g : (-7, " ) - R, and let U be the subspace of W spanned by the functions g1, 92, 93, 94 E W defined by 1 g1 (x) = 1 + sin(x) ' 92(x) = g1(-), 93(x) = 1, 94(x) = tan (x). Using the identity 2 tan (x) = + - 2, 1 + sin(x) 1 - sin(x) find a spanning set for U consisting of three functions. Check