Concept of A Vector Space and Abstract Algebra Discussion

I am looking for help with making a discussion post for my class below is the topic.

This learning module introduced the concept of a vector space. A vector space is a collection of vectors and 2 operators that satisfy 10 axioms. For this discussion, select one of the following prompts:

  1. Five examples of vector spaces were provided without proof in the overview. In this discussion, you will verify axioms of these standard vector spaces. For your initial post, select one of the example vector spaces and verify 4 of the vector space axioms. In responding to your classmates’ posts, verify that their original work is correct, and verify an additional 2 axioms.
  2. Propose your own vector space. Select 4 of the vector space axioms and verify that they do (or do not) hold. In responding to your classmates’ posts, verify that their original work is correct and show that 2 additional axioms do (or do not) hold.

Regardless of which option you select, make sure to clearly explain and justify your work. Also, for consistency, please make sure to number your axioms using the same numbers as the overview/text.

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