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The set of all polynomials of degree 6 under the standard addition and scalar multiplicatior operations is not a vector because * space 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. 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)

The set of all polynomials of degree 6 under the standard addition and scalar multiplicatior operations is not a vector because * space 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. 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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 47E
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The set of all polynomials of degree 6 under the standard addition and scalar multiplication operations is not a vector because * space 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(xsuch that (c+d)P(x)#cP(x)+dP(x). O We can find a polynomial P(x) for which 1-P(x)#P(x) I et A and B be two matrices of size 3 x 3 such that det(A) = 2 and det(B) = 3 Ther
Transcribed Image Text:The set of all polynomials of degree 6 under the standard addition and scalar multiplication operations is not a vector because * space 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(xsuch that (c+d)P(x)#cP(x)+dP(x). O We can find a polynomial P(x) for which 1-P(x)#P(x) I et A and B be two matrices of size 3 x 3 such that det(A) = 2 and det(B) = 3 Ther
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