Which can now be thought of as a set of vectors

Reference no: EM13498901

A set in the plane - which can now be thought of as a set of vectors - is called a convex set if the following holds: Whenever ~u and ~v belong to the set, so does λ~u + (1 - λ)~v for any scalar λ between 0 and 1. Consider the rectangular set Ra,b with one corner at the origin and the "far" corner at the point ha, bi which is in the positive (first) quadrant. Explicitly Ra,b = {hx, y | 0 ≤ x ≤ a, 0 ≤ y ≤ b}.
Use the above definition to show that Ra,b is a convex set.

Reference no: EM13498901

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