1) Let V = Q3[x] and let W = Q2[x]. Consider the transformation T: V → W defined by (a) d T(f) = 3f-2(x + 1)- d² dx dx2f Compute the matrix [T] with respect to the bases B = C = (1, x, x²) (1,x, x², x³) and (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] = 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) = 3f-2(x + 1)- d² dx dx2f Compute the matrix [T] with respect to the bases B = C = (1, x, x²) (1,x, x², x³) and (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] = 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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could you please provide simple answer (explanation too if necessary) for a,b,c. Thank you
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