Operations with Vector Functions

    The following operations give rise to new vector-functions using component-wise operations on vectors.

Definition (Operations with Vector-Valued Functions) Let and be vector-valued functions of the real variable , and let be a real-valued function. Then and are defined as follows:







These operations are defined on the intersection of the domain of the vector-valued and real-valued functions that occur in the definitions, respectively.

Example (Operations with Vector-Valued Functions)  Given and find the vector function

    Solution. We have
    

    






Example (Operations with Vector-Valued Functions)  Given the vector-valued functions







find


     Solution. We have,









Example (Operations with Vector-Valued Functions)  Given the vector-valued functions







find


     Solution. We have,








  

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Cite this as:
Operations With Vector Functions
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/operations-with-vector-functions.html