Determine if the given set is a subspace of Pg. Justify your answer. All polynomials of degree at most 6, with positive real numbers as coefficients. Complete each statement below. The zero vector of P The set The set Is the set a subspace of Pg? O No OYes in the set because zero a positive real number. closed under vector addition because the sum of two positive real numbers closed under multiplication by scalars because the product of a scalar and a positive real number a positive real number. a positive real number.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Determine if the given set is a subspace of Pg. Justify your answer.
All polynomials of degree at most 6, with positive real numbers as coefficients.
Complete each statement below.
The zero vector of P
The set
The set
Is the set a subspace of P?
O No
O Yes
in the set because zero
a positive real number.
closed under vector addition because the sum of two positive real numbers m a positive real number.
closed under multiplication by scalars because the product of a scalar and a positive real number
a positive real number.
Transcribed Image Text:Determine if the given set is a subspace of Pg. Justify your answer. All polynomials of degree at most 6, with positive real numbers as coefficients. Complete each statement below. The zero vector of P The set The set Is the set a subspace of P? O No O Yes in the set because zero a positive real number. closed under vector addition because the sum of two positive real numbers m a positive real number. closed under multiplication by scalars because the product of a scalar and a positive real number a positive real number.
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