Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X + X2, X2 + X3, X3}. (You don't have to prove that C is indeed a basis of V). Show what the image under fC is of: • the four basic elements: Q1(X) = 1 + X, Q2(X) = X + X2, Q3(X) = X2 +X3 and Q4(X) = X3 • P(X) = 2 + 6X + 3X2 + 4X3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X + X2, X2 + X3, X3}. (You don't have to prove that C is indeed a basis of V). Show what the image under fC is of:
• the four basic elements: Q1(X) = 1 + X, Q2(X) = X + X2, Q3(X) = X2 +X3 and Q4(X) = X3

• P(X) = 2 + 6X + 3X2 + 4X3
.

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