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Solve the problem. Let H be the set of all polynomials having degree at most 4...

Question

Solve the problem. Let H be the set of all polynomials having degree at most 4...

Solve the problem. Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H

Solve the problem. Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether His a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy A: Contains zero vector B: Closed under vector addition C Closed under multiplication by scala His not a vector space, not dosed under multiplication to scalars His a vector space His not a vector space:not closed under vector addition O H is not a vector space does not contain zece vector Moving to another question will save this response

Answers

Here Field of vector space is not defined.

Suppose , here Field is of real numbers which contains both rationals and irrational numbers....

Therefore if we multiply an irrational number to any non zero polynomial then it's coefficients becomes irrationals and polynomial further does not belongs to the set of polynomials of degree at most 4 with rational coefficients....i.e. this is not closed under scalar multiplication.....

And H is not a vector space.

Statements A and B are true but C is false.


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