Let x, y, u and v be row vectors in R obeying: x = (2, –1, 3), y = (-3, 2, 2), and suppose that X . w = 7, y.w = -2, and uxv= (4,-2, 4). Use this information to answer the following questions: a) Calculate (x X y) x w. b) Find (x X v) u. c) Calculate (2u – 5v) x (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectorsu+ kv and ku + v is 48 for some k ER.What are the possible values of k?

Let x, y, u and v be row vectors in R obeying: x = (2, –1, 3), y = (-3, 2, 2), and suppose that X . w = 7, y.w = -2, and uxv= (4,-2, 4). Use this information to answer the following questions: a) Calculate (x X y) x w. b) Find (x X v) u. c) Calculate (2u – 5v) x (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectorsu+ kv and ku + v is 48 for some k ER.What are the possible values of k?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 18EQ

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