The set of all polynomials of degree 4 under the standard addition and scalar multiplication operations is not a vector space because * O We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x) O It is not closed under addition. O We can find a polynomial P(x) for which 1-P(x)#P(x) O We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x).

The set of all polynomials of degree 4 under the standard addition and scalar multiplication operations is not a vector space because * O We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x) O It is not closed under addition. O We can find a polynomial P(x) for which 1-P(x)#P(x) O 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 44EQ

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