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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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.
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