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False 1. If v, w, x E R" are vectors with v · w = 0 and w· x = 0, then v•x = 0 too. False 2. If v, w e R" are vectors with |v· w| < 1, then ||v|| < 1 or ||w|| < 1 (or both). True 3. There exist vectors v, w ER' such that ||v|| = 1, ||w|| = 2, and v ·w = -1. True 4. If v, w, x E R" are vectors with v · w = v• X, then w = x. False 5. If v, w E R" are vectors with ||v|| + ||w|| < 2, then ||v + w|| < 2 too.

False 1. If v, w, x E R" are vectors with v · w = 0 and w· x = 0, then v•x = 0 too. False 2. If v, w e R" are vectors with |v· w| < 1, then ||v|| < 1 or ||w|| < 1 (or both). True 3. There exist vectors v, w ER' such that ||v|| = 1, ||w|| = 2, and v ·w = -1. True 4. If v, w, x E R" are vectors with v · w = v• X, then w = x. False 5. If v, w E R" are vectors with ||v|| + ||w|| < 2, then ||v + w|| < 2 too.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
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i believe there are 2 wrong. please correct them and provide some explanation too. thank you.

False 1. If v, w, x E R" are vectors with v · w = 0 and w •x = 0, then v· x = 0 too. False 2. If v, w E R" are vectors with |v· w| < 1, then ||v|| < 1 or ||w|| < 1 (or both). True 3. There exist vectors v, w E R' such that ||v|| = 1, ||w|| = 2, and v · w = -1. %3| %3D True 4. If v, w, x E R" are vectors with v · w = v • X, then w = x. False 5. If v, w E R" are vectors with ||v|| + ||w|| < 2, then ||v + w|| < 2 too.
Transcribed Image Text:False 1. If v, w, x E R" are vectors with v · w = 0 and w •x = 0, then v· x = 0 too. False 2. If v, w E R" are vectors with |v· w| < 1, then ||v|| < 1 or ||w|| < 1 (or both). True 3. There exist vectors v, w E R' such that ||v|| = 1, ||w|| = 2, and v · w = -1. %3| %3D True 4. If v, w, x E R" are vectors with v · w = v • X, then w = x. False 5. If v, w E R" are vectors with ||v|| + ||w|| < 2, then ||v + w|| < 2 too.
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