The set of all polynomials of degree 6 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 two polynomials P(x) O and Q(x) for which P(x)-Q(x)=Q(x)·P(x) We can find a polynomial P(x) for which 1-P(x)=P(x) It is not closed under addition.

The set of all polynomials of degree 6 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 two polynomials P(x) O and Q(x) for which P(x)-Q(x)=Q(x)·P(x) We can find a polynomial P(x) for which 1-P(x)=P(x) It is not closed under addition.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.5: Applications

Problem 30EQ

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