The set of all polynomials of degree 7 under the standard addition and scalar multiplicationoperations is not a vectorspacebecause *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.

Suppose P7=f(x) | f(x) is a polynomial of degree 7. Then we have to check why this set is not a…

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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