The set of all polynomials of degree 6 under -he standard addition and scalar multiplication pperations is not a vector space because We can find two polynomials P(x) 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) OIt is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).

The set of all polynomials of degree 6 under -he standard addition and scalar multiplication pperations is not a vector space because We can find two polynomials P(x) 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) OIt is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 61EQ

See similar textbooks