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be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1², P2(x) 2+x+1², P3(x) = 2+x², P4(x) = choose 11+ 3x + 6x² and let C = (P1(x), P2(x), P3(x), P4(x)}. a. Use coordinate representations with respect to the basis B = {1, 2, 2², 2³} to determine whether the set C forms a basis for P b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials. 10

be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1², P2(x) 2+x+1², P3(x) = 2+x², P4(x) = choose 11+ 3x + 6x² and let C = (P1(x), P2(x), P3(x), P4(x)}. a. Use coordinate representations with respect to the basis B = {1, 2, 2², 2³} to determine whether the set C forms a basis for P b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials. 10

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. {}
Transcribed Image Text: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. {}
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