Is V a vector space over F if the following conditions are given?
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Can you help me figure this out,... Let V denote the set of all m x n matrices with real entities; so V is a vector space over R (given by the book). Let F be the field of rational numbers. Is V a vector space over F with the usual definitions of matrix addition and scalar multiplication... For A, B are in M(mxn) (F) and c is in F, (A + B)ij = Aij + Bij and (cA)ij = cAij
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Answer:
Yes, V is a vector space over F, as the operations defined is standard matrix addition and multiplication by a scalar.
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