Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, C2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion

Consider the set V of all real triples of the form (a, b, c) where c = a - 2b under the usual vector addition and scalar multiplication of R3 Let v1 = (a1, b1, C1), v2 =(a2, b2, C2), be vectors in set V as needed (pay attention to the definition of vectors in this set, i.e. the relationship between c and the other components -- it should be incorporated in your proof.), and let k be a scalar. Either: prove that this set V is a subspace of R or show that V is not a vector subspace by giving a counter example to a required condition. Be clear in what you need to show; show it; and then state your conclusion

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

See similar textbooks