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Determine if the given set is a subspace of Pn for an appropriate value of n. All polynomials in Pn such that p(0) = 0?

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Final answer:

The given set of polynomials in Pn such that p(0) = 0 is a subspace of Pn.

Step-by-step explanation:

In order to determine if the given set is a subspace of Pn, we need to check if it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

For the given set, which consists of all polynomials in Pn such that p(0) = 0, we can see that it satisfies these properties. Adding two polynomials with zero constant term will also have a zero constant term, and multiplying a polynomial by a scalar will still have a zero constant term. Additionally, the zero polynomial satisfies p(0) = 0, so it is in the set.

Therefore, the given set is indeed a subspace of Pn.

User Belvi Nosakhare
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