Consider the vector space Rn, and let v = (v1,v2,...,vn) and w = (w1,w2,...,wn) be vectors in Rn. Complete the proof begun in Example 5.1.6 that the mapping , defined by v, w = k1v1w1 + k2v2w2 ++ knvnwn is a valid inner product on Rn if and only if the constants k1, k2,..., kn are all positive

Chapter 1 Summary 1.1 The Real Number System Common Subsets of Real Numbers p. 34 The sets N, Z, Q, and R, as well as whole numbers and irrational numbers N: Natural Numbers (or Counting) N= {1, 2, 3, 4, 5, …} The set is infinite, so in list form we can write only the first few numbers. Whole: {0, 1, 2, 3, 4, 5, …} Whole numbers are natural...