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1. Check that the following functions on R² are norms: 1/p a) || (x1, #2) ||,= ( 1z1P + \zal" ) b) || (11, x2) ||= max{ |r1\, |#2|

1. Check that the following functions on R² are norms: 1/p a) || (x1, #2) ||,= ( 1z1P + \zal" ) b) || (11, x2) ||= max{ |r1\, |#2|

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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1. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1sp<c. 1<p<o0. b) || (x1, x2) ||= max
Transcribed Image Text:1. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1sp<c. 1<p<o0. b) || (x1, x2) ||= max
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