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(a) Let a, b e V and suppose that ||b+a|| = 0 and ||b – a|| = 0. What can be said about a, b? Prove your claim. %3| (b)Prove that for all vectors a, b E V, |||b|| – ||a||| < ||b – a|l. (c)Give an example of a normed vector space V and a pair of vectors a, b E V such that |la – b|| 4 ||a|| – |B||.

(a) Let a, b e V and suppose that ||b+a|| = 0 and ||b – a|| = 0. What can be said about a, b? Prove your claim. %3| (b)Prove that for all vectors a, b E V, |||b|| – ||a||| < ||b – a|l. (c)Give an example of a normed vector space V and a pair of vectors a, b E V such that |la – b|| 4 ||a|| – |B||.

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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please solve these 2 for me im begging you please thank you

7. (a) Let a, bE V and suppose that ||b+al = 0 and ||b– a|| = 0. What can be said about a, b? Prove your claim. (b)Prove that for all vectors a, b E V, ||b|| – ||a||| < ||b – a|l. (c)Give an example of a normed vector space V and a pair of vectors a, b E V such that |la – b|| 4 ||a|| – |||.
Transcribed Image Text:7. (a) Let a, bE V and suppose that ||b+al = 0 and ||b– a|| = 0. What can be said about a, b? Prove your claim. (b)Prove that for all vectors a, b E V, ||b|| – ||a||| < ||b – a|l. (c)Give an example of a normed vector space V and a pair of vectors a, b E V such that |la – b|| 4 ||a|| – |||.
8. Decide whether or not the Cauchy-Schwartz inequality is true in R?, with the norm defined by (a) ||2|| = |x| + |r2|, (b) ||2||= max{|x1|, |&2]}, where r = (x1, x2).
Transcribed Image Text:8. Decide whether or not the Cauchy-Schwartz inequality is true in R?, with the norm defined by (a) ||2|| = |x| + |r2|, (b) ||2||= max{|x1|, |&2]}, where r = (x1, x2).
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