Consider the vector space Rn. Let u = (u1, ... , un) be a vector in Rn. Prove that both
Chapter 1, Problem 38(choose chapter or problem)
Consider the vector space Rn. Let u = (u1, ... , un) be a vector in Rn. Prove that both the following satisfy the properties of norm mentioned in Exercise 37. These expressions, even though they do not lead to Euclidean geometry , have all the algebraic properties we expect a norm to have and are used in numerical mathematics. (a) llull = lu1I + + lunl sum of magnitudes norm (b) llull =.max lunl maximummagnitude =l. .. n norm (c) Compute these two norms for the vectors (1, 2), (- 3, 4), (1, 2, -5), (0, -2, 7).
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