could you please just give a simple explanation for parts d & e 1) Let V = Q3[x] and let W = Q₂ [x]. Consider the transformation T: V → W definedbydT(f) = 3f-2(x + 1)₂d²dx(a)dx25Compute the matrix [T] with respect to the bases B = (1, x, x², x³) andC = (1, x, x²)(b)Compute the matrix [T]g, with respect to the basis B' = (1, x+1, x² +1, x³ +1)and C = (1,x+1, x² + 1)(c) Compute the change of basis matrix P from B to B'(d) Compute the change of basis matrix Q from C to C'(e) Compute P-1 and verify the formula [T]g, = Q[T]&P-1

Answered: Image /qna-images/answer/7d4f0421-4a0a-4096-9a27-337b21f49d35.jpg

1) Let V = Q3 [x] and let W = Q2 [x]. Consider the transformation T: V → W defined by (a) d T(f) = 3—ƒ-2(x+1) f dx Compute the matrix [7] with respect to the bases B = (1, x, x², x³) and C = (1, x, x²) d² (b) Compute the matrix [T]g, with respect to the basis B' = (1, x+1, x² +1, x³+1) and C = (1,x+1, x² + 1) (c) Compute the change of basis matrix P from B to B' (d) Compute the change of basis matrix Q from C to C' (e) Compute P-1 and verify the formula [T]g, = Q[T]&P-¹

1) Let V = Q3 [x] and let W = Q2 [x]. Consider the transformation T: V → W defined by (a) d T(f) = 3—ƒ-2(x+1) f dx Compute the matrix [7] with respect to the bases B = (1, x, x², x³) and C = (1, x, x²) d² (b) Compute the matrix [T]g, with respect to the basis B' = (1, x+1, x² +1, x³+1) and C = (1,x+1, x² + 1) (c) Compute the change of basis matrix P from B to B' (d) Compute the change of basis matrix Q from C to C' (e) Compute P-1 and verify the formula [T]g, = Q[T]&P-¹

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 22EQ

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