Question

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For thos

Rational functions
ANSWERED
asked 2021-05-14
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).

Expert Answers (1)

2021-05-15
The degree restriction for f and g has no effect on satisfaction of any axioms. As that condition will be satisfied even if we add two rational functions of same type or if we multiply some real number to a rational function of that type. And inclusion of f=0 implies that axiom 5 and axiom 6 hold.
2 Therefore all axioms are satisfied similar to exercise 1(refer previous solution).
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