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p(0) p(1) p(2) 7. Let the linear transformation T : P2 → R³ be defined by T(p(x)) = and let %3D B = {1,x,x²} and D = 0 0 Show that MpB(T) = 1 1 1 and deduce that T is an isomorphism. %3D 1 2 4 1 |= 2, implying that MpB(T) is invertible. Therefore, T 1 Solution. det MDB(T) = det 2 4 is an isomorphism.

p(0) p(1) p(2) 7. Let the linear transformation T : P2 → R³ be defined by T(p(x)) = and let %3D B = {1,x,x²} and D = 0 0 Show that MpB(T) = 1 1 1 and deduce that T is an isomorphism. %3D 1 2 4 1 |= 2, implying that MpB(T) is invertible. Therefore, T 1 Solution. det MDB(T) = det 2 4 is an isomorphism.

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 explain to me why in this question T(1)=<1,1,1> T(x)=<0,2,1> and T<x^2>=<0,4,1>?I need the detailed explanation.Thank you.

p(0) p(1) p(2) 7. Let the linear transformation T : P2 → R³ be defined by T(p(x)) = and let B = {1,x,x²} and D = 0 0 Show that MpB(T) = 1 1 1 and deduce that T is an isomorphism. %3D 1 2 4 1 Solution. det MDB(T) = det 2 1 2, implying that MpB(T) is invertible. Therefore, T 4 is an isomorphism.
Transcribed Image Text:p(0) p(1) p(2) 7. Let the linear transformation T : P2 → R³ be defined by T(p(x)) = and let B = {1,x,x²} and D = 0 0 Show that MpB(T) = 1 1 1 and deduce that T is an isomorphism. %3D 1 2 4 1 Solution. det MDB(T) = det 2 1 2, implying that MpB(T) is invertible. Therefore, T 4 is an isomorphism.
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