The set of all polynomials of degree † under the standard addition and scalar multiplication operations is not a vector space because * We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). We can find a polynomial P(x) for which 1-P(x)#P(x) We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x) It is not closed under addition.
The set of all polynomials of degree † under the standard addition and scalar multiplication operations is not a vector space because * We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). We can find a polynomial P(x) for which 1-P(x)#P(x) We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x) It is not closed under addition.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 10E
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Transcribed Image Text:The set of all polynomials of degree 7 under the standard addition and scalar multiplication
operations is not a vector
space
because *
O We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).
OWe can find a polynomial P(x) for which 1 P(x)#P(x)
We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x)
It is not closed under addition.
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