Let V be a vector space and let V1, V2, V3 be vectors in V. Define the set S and S' by S = {v1, V2, V3}, S' = {v1 + V2, Vị – 2v2, Vị + V2 + V3} . (a) Show that span (S) = span (S'). (b) Show that the set S is linearly independent if and only if the set S' is linearly independent.
Let V be a vector space and let V1, V2, V3 be vectors in V. Define the set S and S' by S = {v1, V2, V3}, S' = {v1 + V2, Vị – 2v2, Vị + V2 + V3} . (a) Show that span (S) = span (S'). (b) Show that the set S is linearly independent if and only if the set S' is linearly independent.
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 V be a vector space and let v1, V2, V3 be vectors in V. Define the set S and S' by
S = {v1, v2, V3} ;
{Vì + V2, V1 – 2v2, V1 + V2 + V3} .
(a) Show that span (S) = span (S').
(b) Show that the set S is linearly independent if and only if the set S' is linearly independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1010c5bc-8d0d-4294-b41e-dc78670bcca8%2Fbc8301d8-20de-4c43-bbf3-47adc84cca0e%2F3094bc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let V be a vector space and let v1, V2, V3 be vectors in V. Define the set S and S' by
S = {v1, v2, V3} ;
{Vì + V2, V1 – 2v2, V1 + V2 + V3} .
(a) Show that span (S) = span (S').
(b) Show that the set S is linearly independent if and only if the set S' is linearly independent.
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