Answered: (a) Show that the list {p o(x), p 1(x),… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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2. (a) Show that the list {p o(x),p 1(x), p 2(x),... ,P n(x),...,} where
Po(x) = 1, p1(x) = 1+x,
P;(x) = 1+x +
+ x³,
•..)
is a basis of the vector space F[x] of all polynomials with coeficients in F.
(b) What are the coordinates of the vector x" relative to the basis (po(x),P1(x),..., P; (x),...)?

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{ƒf(x) = P₂[x] |ƒ'(−8) =ƒ(1)} where P₂[x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x². p(x) = ,q(x) = =
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Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let = 2+x+x², 2+x+x², 2+x², = 11 + 3x + 6x² choose PI(T) P2(x) P3(x) = P4(x) and let C = {p1(x), p2(x), P3(x), P4(x)}. a. Use coordinate representations with respect to the basis B = {1, 2, ², ³} to determine whether the set C forms a basis for P.. = c. The dimension of span(C) is b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials. {}
2. (a) Show that the list {p o(x), p 1(x), p 2(x),...,p n(x),...,} where Po(x) = 1, P₁(x) = 1 + x, pj(x) = 1 + x + · +x², is a basis of the vector space F[x] of all polynomials with coeficients in F. (b) What are the coordinates of the vector xn relative to the basis (po(x), p₁(x),..., pj(x), ...)?
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