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5. Let P2(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C3 be the vector space over C. By using linear extension method, show that P₂(C) = C³.

5. Let P2(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C3 be the vector space over C. By using linear extension method, show that P₂(C) = C³.

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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5. Let P₂(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C³ be the vector space over C. By using linear extension method, show that P₂(C) = C³. 6. Let P₁(C) be the vector space of polynomials of degree less than or equal to 1 over R and C³ be the vector space over R. Let a = {1,i, x, zi} be the basis for P₂ (C) and 3 = {(1, 1, 1), (2, 3,0), (i, 1,0), (0, 0, i)} be arbitrary vectors in C³. Determine whether linear transformation T: P₁(C) → C³ exists by using linear extension method.
Transcribed Image Text:5. Let P₂(C) be the vector space of polynomials of degree less than or equal to 2 over C. Let C³ be the vector space over C. By using linear extension method, show that P₂(C) = C³. 6. Let P₁(C) be the vector space of polynomials of degree less than or equal to 1 over R and C³ be the vector space over R. Let a = {1,i, x, zi} be the basis for P₂ (C) and 3 = {(1, 1, 1), (2, 3,0), (i, 1,0), (0, 0, i)} be arbitrary vectors in C³. Determine whether linear transformation T: P₁(C) → C³ exists by using linear extension method.
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