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Task 2: Let f(x), g(x), h(x), i(x) EP be polynomials f(x) = 1+4x³, g(x)=2+x+2x³, h(x) = 3+2x, i(x) = 1 + x − 2x³. (a) Find a base in the span u = span{f, g, h, i}. (b) What is the dimension of u? (c) What are the coordinates of 2 + 2x - 4x³ in the base you found in (a).

Task 2: Let f(x), g(x), h(x), i(x) EP be polynomials f(x) = 1+4x³, g(x)=2+x+2x³, h(x) = 3+2x, i(x) = 1 + x − 2x³. (a) Find a base in the span u = span{f, g, h, i}. (b) What is the dimension of u? (c) What are the coordinates of 2 + 2x - 4x³ in the base you found in (a).

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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Task 2: Let f(x), g(x), h(x), i(x) € P be polynomials f(x)=1+4x³, g(x) = 2+x+2x³, h(x)=3+2x, i(x)=1+x-2x³. (a) Find a base in the span u = span{f, g, h, i}. (b) What is the dimension of u? (c) What are the coordinates of 2 + 2x - 4x³ in the base you found in (a).
Transcribed Image Text:Task 2: Let f(x), g(x), h(x), i(x) € P be polynomials f(x)=1+4x³, g(x) = 2+x+2x³, h(x)=3+2x, i(x)=1+x-2x³. (a) Find a base in the span u = span{f, g, h, i}. (b) What is the dimension of u? (c) What are the coordinates of 2 + 2x - 4x³ in the base you found in (a).
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