Solved: Consider the points in Exercise 5 in Section 8.1.

Chapter 8, Problem 3E

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Problem 3E

Consider the points in Exercise 5 in Section 8.1. Which of p1, p2, and p3 are in conv S?

Reference Exercise 5 in Section 8.1:

In Exercises 5 and 6, let

Note that S is an orthogonal basis for R3. Write each of the given points as an affine combination of the points in the set S, if possible. [Hint: Use Theorem 5 in Section 6.2 instead of row reduction to find the weights.]

Reference Theorem 5 in Section 6.2:

An m × n matrix U has orthonormal columns if and only if UTU = I .