If ||2x - y < 2 and ly| < 1, prove that | x-yll2-x.x < 2. If n = 3, x 3. yll
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 answer d
Transcribed Image Text:EXERCISES
8.1.1. Let x, y, z € R".
a) If ||xz|| <2 and ly-z|| <3, prove that ||x-y| < 5.
b) If ||x|| <2, |ly|| <3, and ||z|| < 4, prove that x-y-x-z< 14.
c) If |x-y|| <2 and ||z|| <3, prove that ix- (y-z)-y. (x-2)| < 6.
d) If ||2x -y|| < 2 and ly|| < 1, prove that | ||x-y||2-x-x/ < 2.
e) If n = 3, ||xy|| <2, and ||z|| <3, prove that ||xx z-y x z|| < 6.
f) If n = 3, ||x|| < 1, ly| < 2, and ||z|| <3, prove that ||x (y xz) || < 6.
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