Question

Determine if the given set is a subspace of $P_n$. Justify your answer. The set of all polynomials in $P_n$ such that $p(0) = 0$ Choose the correct answer below. A. The set is not a subspace of $P_n$ because the set is not closed under multiplication by scalars. B. The set is not a subspace of $P_n$ because the set is not closed under vector addition. C. The set is a subspace of $P_n$ because $P_n$ is a vector space spanned by the given set. D. The set is not a subspace of $P_n$ because the set does not contain the zero vector of $P_n$ E. The set is a subspace of $P_n$ because the set contains the zero vector of $P_n$, the set is closed under vector addition, and the set is closed under multiplication by scalars.

          Determine if the given set is a subspace of $P_n$. Justify your answer.
The set of all polynomials in $P_n$ such that $p(0) = 0$
Choose the correct answer below.
A. The set is not a subspace of $P_n$ because the set is not closed under multiplication by scalars.
B. The set is not a subspace of $P_n$ because the set is not closed under vector addition.
C. The set is a subspace of $P_n$ because $P_n$ is a vector space spanned by the given set.
D. The set is not a subspace of $P_n$ because the set does not contain the zero vector of $P_n$
E. The set is a subspace of $P_n$ because the set contains the zero vector of $P_n$, the set is closed under vector addition, and the set is closed under multiplication by scalars.

Determine if the given set is a subspace of Pn. Justify your answer.
The set of all polynomials in Pn such that p(0) = 0
Choose the correct answer below.
A. The set is not a subspace of Pn because the set is not closed under multiplication by scalars.
B. The set is not a subspace of Pn because the set is not closed under vector addition.
C. The set is a subspace of Pn because Pn is a vector space spanned by the given set.
D. The set is not a subspace of Pn because the set does not contain the zero vector of Pn
E. The set is a subspace of Pn because the set contains the zero vector of Pn, the set is closed under vector addition, and the set is closed under multiplication by scalars.

Added by Marcos M.

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