Let V be the set of vectors shown below. V= a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in V, is u + v in V? O A. The vector u + v must be in V because V is a subset of the vector space R?. O B. The vector u + v must be in V because the x-coordinate of u + v is the sum of two negative numbers, which must also be negative, and the y-coordinate of u + v is the sum of positive numbers, which must also be positive. OC. The vector u + v may or may not be in V depending on the values of x and y. O D. The vector u + v is never in V because the entries of the vectors in V are scalars and not sums of scalars.

Let V be the set of vectors shown below. V= a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in V, is u + v in V? O A. The vector u + v must be in V because V is a subset of the vector space R?. O B. The vector u + v must be in V because the x-coordinate of u + v is the sum of two negative numbers, which must also be negative, and the y-coordinate of u + v is the sum of positive numbers, which must also be positive. OC. The vector u + v may or may not be in V depending on the values of x and y. O D. The vector u + v is never in V because the entries of the vectors in V are scalars and not sums of scalars.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 21EQ

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