Final answer:
The set {tv + (1 − t)w : t ∈ [0, 1]} illustrates all points on the line segment between vectors v and w. For any t in the interval [0, 1], a corresponding point on the line segment is created by linearly interpolating between v and w.
Step-by-step explanation:
The set {tv + (1 − t)w : t ∈ [0, 1]} represents all the linear combinations of vectors v and w for scalar values of t between 0 and 1. When t is 0, the vector equals w, and when t is 1, it equals v; for other values of t, you get points that are on the straight line joining v to w, essentially interpolating between them. This is because the expression t scales vector v and (1-t) scales vector w, and their sum constitutes a line segment's equation where t dictates the contribution of each endpoint vector to the intermediate points.