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In a vector space V, prove that Ov=0 for all v € V. Let u = (1, 2, -1), v = (6,4,2) € R³. 5.1 Write w = (-3,2,-5) as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is {u, v) a basis for R³? Explain clearly.

In a vector space V, prove that Ov=0 for all v € V. Let u = (1, 2, -1), v = (6,4,2) € R³. 5.1 Write w = (-3,2,-5) as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is {u, v) a basis for R³? Explain clearly.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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In a vector space V, prove that Ov=0 for all v V. Let u = (1, 2, -1), v = (6,4,2) € R³. 5.1 Write w (-3,2,-5) as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is (u, v) a basis for R³? Explain clearly.
Transcribed Image Text:In a vector space V, prove that Ov=0 for all v V. Let u = (1, 2, -1), v = (6,4,2) € R³. 5.1 Write w (-3,2,-5) as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is (u, v) a basis for R³? Explain clearly.
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