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3. In each case suppose R" has the norm ||l inclusions: = max {ril,., r.}. Prove each of the set (a) Ba(1) C Ba(0) in R (b) B2(1, 1) C B3(1,0) in R? (c) B,(3,0,-2) C B,(1, 1,-1) in R* (d) Ba(1,0,0,0) S B(0,0,-1, 1) in R'.

3. In each case suppose R" has the norm ||l inclusions: = max {ril,., r.}. Prove each of the set (a) Ba(1) C Ba(0) in R (b) B2(1, 1) C B3(1,0) in R? (c) B,(3,0,-2) C B,(1, 1,-1) in R* (d) Ba(1,0,0,0) S B(0,0,-1, 1) in R'.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 26E: Prove that the cancellation law for multiplication holds in Z. That is, if xy=xz and x0, then y=z.
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3. In each case suppose R" has the norm |||| inclusions: = max {ril,., r.}. Prove each of the set (a) B3(1) C Ba(0) in IR (b) B2(1, 1) C B3(1,0) in R? (c) B,(3,0,-2) C B,(1, 1,-1) in R (d) B(1,0,0,0) C B(0,0,-1, 1) in R'.
Transcribed Image Text:3. In each case suppose R" has the norm |||| inclusions: = max {ril,., r.}. Prove each of the set (a) B3(1) C Ba(0) in IR (b) B2(1, 1) C B3(1,0) in R? (c) B,(3,0,-2) C B,(1, 1,-1) in R (d) B(1,0,0,0) C B(0,0,-1, 1) in R'.
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