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Let u, w R" with |||| = 2 and |||| 2w = 6v. There are two parts to the proof. Part 1: Suppose 2 = 67. Then = 3 V. Thus || + || = || Part 2: 7|| A. u = kü, k> 0 = 6. Prove that || + || = 8 if and only if w = k ²/7 , k> 0 7 and 7+ w = 7+ ||३|| Suppose || + || = 8. By the triangular inequality, ||+|| ≤ ||v|| + ||w|| = It follows that and w are in the same direction, i.e. Hence 2w = 67. = Q.E.D. C. Where k =

Let u, w R" with |||| = 2 and |||| 2w = 6v. There are two parts to the proof. Part 1: Suppose 2 = 67. Then = 3 V. Thus || + || = || Part 2: 7|| A. u = kü, k> 0 = 6. Prove that || + || = 8 if and only if w = k ²/7 , k> 0 7 and 7+ w = 7+ ||३|| Suppose || + || = 8. By the triangular inequality, ||+|| ≤ ||v|| + ||w|| = It follows that and w are in the same direction, i.e. Hence 2w = 67. = Q.E.D. C. Where k =

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 7, ER" with |||| = 2 and |||| 2w = 60. There are two parts to the proof. Part 1: Suppose 2 = 67. Then = 3 V. Thus || + || = || Part 2: A. w = kü, k> 0 7|| B. w k = k> 0 = 6. Prove that || + || = 8 if and only if Suppose || + || = 8. By the triangular inequality, || + || ≤ ||v|| + ||w|| = 7 and 7+ w = 7+ It follows that and are in the same direction, i.e. Hence 2w = 67. |||| = Q. E. D. ◆. Where k =
Transcribed Image Text:Let 7, ER" with |||| = 2 and |||| 2w = 60. There are two parts to the proof. Part 1: Suppose 2 = 67. Then = 3 V. Thus || + || = || Part 2: A. w = kü, k> 0 7|| B. w k = k> 0 = 6. Prove that || + || = 8 if and only if Suppose || + || = 8. By the triangular inequality, || + || ≤ ||v|| + ||w|| = 7 and 7+ w = 7+ It follows that and are in the same direction, i.e. Hence 2w = 67. |||| = Q. E. D. ◆. Where k =
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