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Question (7) Suppose {X} is a sequence of points (vectors) in R" converging to a. (a) Prove that ||XK|| → ||a||. (b) Prove that if b E R" is any vector, then b. Xkb.a.

Question (7) Suppose {X} is a sequence of points (vectors) in R" converging to a. (a) Prove that ||XK|| → ||a||. (b) Prove that if b E R" is any vector, then b. Xkb.a.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Question (7) Suppose {X} is a sequence of points (vectors) in R" converging to a. (a) Prove that ||X|| → ||a||. (b) Prove that if bER" is any vector, then b. Xk → b.a. Question (8) Prove that f: R" → R, f(X) = ||X|| is continuous. moreover, every norm is a continu- ous function.
Transcribed Image Text:Question (7) Suppose {X} is a sequence of points (vectors) in R" converging to a. (a) Prove that ||X|| → ||a||. (b) Prove that if bER" is any vector, then b. Xk → b.a. Question (8) Prove that f: R" → R, f(X) = ||X|| is continuous. moreover, every norm is a continu- ous function.
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