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P 3 is a vector space of polynomials in x of degree three or less and Dx(p(x)) = the derivative of p(x) is a transformation from P 3 to P 2.

a. the nullity of Dx is two.
b. The polynomial 2x + 1 is in the kernel of Dx.
c. The polynomial 2x + 1 is in the range of Dx.
d. The kernel of Dx is all those polynomials in P 3 with zero constant term.
e. The rank of Dx is three.

Please explain the reasoning behind the proper choice.

Thank you.

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Solution Summary

The polynomial is clearly evaluated in this case.

Solution Preview

The correct answer is c. The polynomial 2x+1 is in the range of Dx.
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