Question

- Explain the general relationship between abstract algebra and linear algebra.
- Discuss how it is possible to considerably shorten the list of properties that define a vector space by using definitions from abstract algebra.

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* Explain the general relationship between abstract algebra and linear algebra.

Linear algebra studies the properties and structure of the vector spaces. A vector space V over a field F, is a set together with two binary operations (+,∙ ) that satisfy a list of axioms. The elements of V are called vectors while the elements of F are scalars. Abstract algebra generalizes this notion of a vector space over a field by the study of modules over a ring....

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