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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

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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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 defined by d T(f) = 3f-2(x + 1)₂ d² dx (a) dx25 Compute the matrix [T] with respect to the bases B = (1, x, x², x³) and C = (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
Transcribed Image Text:1) Let V = Q3[x] and let W = Q₂ [x]. Consider the transformation T: V → W defined by d T(f) = 3f-2(x + 1)₂ d² dx (a) dx25 Compute the matrix [T] with respect to the bases B = (1, x, x², x³) and C = (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
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