Let || - || be a norm on a linear space X. if x, y= X and ||x + y|| = ||x||+||y||, then show that ||sx + ty|| = s||x|| + t||y|| for all s≥0, t≥0.
Let || - || be a norm on a linear space X. if x, y= X and ||x + y|| = ||x||+||y||, then show that ||sx + ty|| = s||x|| + t||y|| for all s≥0, t≥0.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 55E: Let T be a linear transformation from P2 into P2 such that T(1)=x,T(x)=1+xandT(x2)=1+x+x2. Find...
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![Let || - || be a norm on a linear space X. if x, y= X and ||x + y|| = ||x||+||y||, then show
that ||sx + ty|| = s||x|| + t||y|| for all s≥0, t≥0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15b7304-cc73-4505-92c3-23aa2fda4f71%2F4d5be0a4-ceaf-40df-906c-b84ed1be3f15%2Fn9b6isb_processed.png&w=3840&q=75)
Transcribed Image Text:Let || - || be a norm on a linear space X. if x, y= X and ||x + y|| = ||x||+||y||, then show
that ||sx + ty|| = s||x|| + t||y|| for all s≥0, t≥0.
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