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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3664d0c-f1ed-46e5-b912-d3c2e940a1ac%2Fa1fd81a0-8757-457b-a8c9-b148069a4148%2Flon7035_processed.jpeg&w=3840&q=75)
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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