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✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect to B, B where B = (1, x,...,x"), given by ao + a₁x + a₂x²+...+ a₁x² → a₁ + 2a₂x +...+na₂x¹-1 (b) : PnPn+1 with respect to B₁, B₁+1 where B₁ = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ªox + ²x²+...+; an -X^²+1 n+1 (c) : P₁ → R with respect to B, &, where B = (1, x,...,xn) and ₁ = (1), given by ao + a₁x + a₂x²+.... +anx→ao+ ++ an n+1

✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect to B, B where B = (1, x,...,x"), given by ao + a₁x + a₂x²+...+ a₁x² → a₁ + 2a₂x +...+na₂x¹-1 (b) : PnPn+1 with respect to B₁, B₁+1 where B₁ = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ªox + ²x²+...+; an -X^²+1 n+1 (c) : P₁ → R with respect to B, &, where B = (1, x,...,xn) and ₁ = (1), given by ao + a₁x + a₂x²+.... +anx→ao+ ++ an n+1

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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Please do part A,B,C,D and please show step by step and explain

(d) eval3: Pn → R with respect to B, E₁ where B = (1, x,...,xn) and ₁ = given by n ao + a₁x + a₂x² + ... + a₂x² → ªo + a₁. 3+ a₂-3². (e) slide 1: Pn → Pn with respect to B, B where B = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ao + α₁ ⋅ (x + 1) +...+ an. (x + 1)n +... ...+ an.3n (1),
Transcribed Image Text:(d) eval3: Pn → R with respect to B, E₁ where B = (1, x,...,xn) and ₁ = given by n ao + a₁x + a₂x² + ... + a₂x² → ªo + a₁. 3+ a₂-3². (e) slide 1: Pn → Pn with respect to B, B where B = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ao + α₁ ⋅ (x + 1) +...+ an. (x + 1)n +... ...+ an.3n (1),
✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect to B, B where B = (1, x,...,x"), given by ao + a₁x + a₂x²+...+ a₁x² → a₁ + 2a₂x +...+na₂x¹-1 (b) : PnPn+1 with respect to B₁, B₁+1 where B₁ = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ªox + ²x²+...+; an -X^²+1 n+1 (c) : P₁ → R with respect to B, &, where B = (1, x,...,xn) and ₁ = (1), given by ao + a₁x + a₂x²+.... +anx→ao+ ++ an n+1
Transcribed Image Text:✓1.22 Represent each linear map with respect to each pair of bases. (a) d/dx: Pn → Pn with respect to B, B where B = (1, x,...,x"), given by ao + a₁x + a₂x²+...+ a₁x² → a₁ + 2a₂x +...+na₂x¹-1 (b) : PnPn+1 with respect to B₁, B₁+1 where B₁ = (1, x,...,x), given by ao + a₁x + a₂x²+...+ anx" → ªox + ²x²+...+; an -X^²+1 n+1 (c) : P₁ → R with respect to B, &, where B = (1, x,...,xn) and ₁ = (1), given by ao + a₁x + a₂x²+.... +anx→ao+ ++ an n+1
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