Need help with this question. Thank you :) Let n be a positive integer, and let B ={V1, V2, ..V,} be a basis for a vector space V.... ,Let c1, c2, ... , Cn E R and define S = {c¡V1, C2V2, ... , C„V,}.Which one of the following statements is true?O a.S is a basis for V iff at least one of the scalars c1, C2, . , Cn is non-zero.O b. S is a basis for V iff none of the scalars c1, C2, . , Cn are zero.c. S is always basis for V, for any choice of the scalars c1, c2, ... , Cn.O d. S is not a basis for V for any choice of the scalars c1, c2, ·... , Cn.

Let n be a positive integer, and let B = {v1, V2, ... , Vn} be a basis for a vector space V. Let c1, c2, ... , c, E R and define S = {c¡V1, c2V2, ... , C„Vn}. Which one of the following statements is true? S is a basis for V iff at least one of the scalars c1, C2, ... , Cn is non-zero. O b. S is a basis for V iff none of the scalars c1, C2, ... , Cn are zero. c. S is always basis for V, for any choice of the scalars c1, c2, ... , Cn. d. S is not a basis for V for any choice of the scalars c1, C2, . , Cn.

Let n be a positive integer, and let B = {v1, V2, ... , Vn} be a basis for a vector space V. Let c1, c2, ... , c, E R and define S = {c¡V1, c2V2, ... , C„Vn}. Which one of the following statements is true? S is a basis for V iff at least one of the scalars c1, C2, ... , Cn is non-zero. O b. S is a basis for V iff none of the scalars c1, C2, ... , Cn are zero. c. S is always basis for V, for any choice of the scalars c1, c2, ... , Cn. d. S is not a basis for V for any choice of the scalars c1, C2, . , Cn.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 33EQ

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