Let B {x² + 2, x² - 4x + 7, -x + 1} be a basis for P₂ and let B' = {x³ + x², x,x+1, x³ + 1} be a basis for P3. Let T: P3 → P2 be the linear transformation defined by x3 = + x² + 3x T (p(x)) = (x + 1)p(x) + p′(1) + [² Find [TB', the matrix representation of T with respect to the basis B of P2 and the basis B' of P3. 2p(t) dt.

Let B {x² + 2, x² - 4x + 7, -x + 1} be a basis for P₂ and let B' = {x³ + x², x,x+1, x³ + 1} be a basis for P3. Let T: P3 → P2 be the linear transformation defined by x3 = + x² + 3x T (p(x)) = (x + 1)p(x) + p′(1) + [² Find [TB', the matrix representation of T with respect to the basis B of P2 and the basis B' of P3. 2p(t) dt.

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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Question

I'm struggling to solve this problem using matrix notation alone, and I'm looking for your guidance. The requirement is to find a solution using only matrix notation, without employing any other methods. Could you please provide me with a detailed, step-by-step explanation using matrix notation to help me understand and solve the problem until we reach the final solution?

can you please do it step by step so I can understand it better

Let B
4. (
{x² + 2, x² - 4x + 7, -x + 1} be a basis for P₂ and let B' =
{x³ + x²,
x,x+1, x³ + 1} be a basis for P3. Let T: P3 → P2 be the linear transformation defined by
x3
-
+ x² +
3x
T (p(x)) = (x + 1)p(x) + p′(1) + [²
Find [T]', the matrix representation of T with respect to the basis B of P2 and the basis B' of P3.
2p(t) dt.

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