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Suppose T: P2→R³ is an isomorphism whose action on a basis for P2 is as follows: 3 T(x²) = 3 3 T-¹ P 9 r Find the inverse transformation T-1 and give its action on a general vector, using x as the variable for the polynomial and p, q, and r as constants. Use the '^' character to indicate an exponent, e.g. px^2-qx+r. = 1 5 T(x+1)=2 T(x²+x+2) = 6 7 0 2

Suppose T: P2→R³ is an isomorphism whose action on a basis for P2 is as follows: 3 T(x²) = 3 3 T-¹ P 9 r Find the inverse transformation T-1 and give its action on a general vector, using x as the variable for the polynomial and p, q, and r as constants. Use the '^' character to indicate an exponent, e.g. px^2-qx+r. = 1 5 T(x+1)=2 T(x²+x+2) = 6 7 0 2

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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Suppose T: P2→R³ is an isomorphism whose action on a basis for P2 is as follows: 3 5 T(x²) = 3 T(x+1)=2 T(x²+x+2) = 6 3 7 P T¹|q = 0 1 Find the inverse transformation I-1 and give its action on a general vector, using x as the variable for the polynomial and p, q, and r as constants. Use the '^' character to indicate an exponent, e.g. px^2-qx+r. r 2
Transcribed Image Text:Suppose T: P2→R³ is an isomorphism whose action on a basis for P2 is as follows: 3 5 T(x²) = 3 T(x+1)=2 T(x²+x+2) = 6 3 7 P T¹|q = 0 1 Find the inverse transformation I-1 and give its action on a general vector, using x as the variable for the polynomial and p, q, and r as constants. Use the '^' character to indicate an exponent, e.g. px^2-qx+r. r 2
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