The set of all polynomials of degree 4 under the standard addition and scalar multiplication operations is not a vector space because * O It is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)•P(x) O we can find a polynomial P(x) for which 1-P(x)#P(x)
The set of all polynomials of degree 4 under the standard addition and scalar multiplication operations is not a vector space because * O It is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)•P(x) O we can find a polynomial P(x) for which 1-P(x)#P(x)
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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![The set of all polynomials of degree 4 under the standard addition and scalar multiplication
operations is not a vector space because *
It is not closed under addition.
We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).
We can find two polynomials P(x) and Q(x) for which P(x): Q(x)#Q(x):P(x)
O We can find a polynomial P(x) for which 1-P(x)#P(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50db17df-2744-4647-84a5-2ef0bddd99e4%2F28440276-d7f8-440e-9023-c77eb4051931%2Frx7hbp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The set of all polynomials of degree 4 under the standard addition and scalar multiplication
operations is not a vector space because *
It is not closed under addition.
We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).
We can find two polynomials P(x) and Q(x) for which P(x): Q(x)#Q(x):P(x)
O We can find a polynomial P(x) for which 1-P(x)#P(x)
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