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Suppose T: P3-M22 is an isomorphism whose action on a basis for P3 is as follows: 33 T(x³ ) =| 3 3 -6 -6 0 4 T(2x2+x) = 1 -2 -1 Т(3) - T(x3 +x² +x+1)= -6 -12 1 Find the inverse transformation T1 and give its action on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the A character to indicate an exponent e.g. рx 2-qх+r.

Suppose T: P3-M22 is an isomorphism whose action on a basis for P3 is as follows: 33 T(x³ ) =| 3 3 -6 -6 0 4 T(2x2+x) = 1 -2 -1 Т(3) - T(x3 +x² +x+1)= -6 -12 1 Find the inverse transformation T1 and give its action on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the A character to indicate an exponent e.g. рx 2-qх+r.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Suppose T: P3-→M22 is an isomorphism whose action on a basis for P3 is as follows: 0 4 T(x3+x²+x+1) = 1 -2 -1 6 3 3 T(x³ ) = 3 3 T(3) = T(2x²+x) = -6 -12 -1 Find the inverse transformation T- and give its action on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the 'A' character to indicate an exponent, e.g. px^2-qx+r.
Transcribed Image Text:Suppose T: P3-→M22 is an isomorphism whose action on a basis for P3 is as follows: 0 4 T(x3+x²+x+1) = 1 -2 -1 6 3 3 T(x³ ) = 3 3 T(3) = T(2x²+x) = -6 -12 -1 Find the inverse transformation T- and give its action on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the 'A' character to indicate an exponent, e.g. px^2-qx+r.
Suppose T: P2-R° is an isomorphism whose action on a basis for P2 is as follows: 1 -3 2 T(x+1)= 2 T(3x²+3x+3)=| 0 T(-x2-1) = |1 2 Find the inverse transformation T1 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 'A' character to indicate an exponent, e.g. px^2-qx+r. = (-4p-29-2r)x²+ p-+tp+q) The correct answer is: 1 T1 글기자2+(-p+r]x+(-p+q)
Transcribed Image Text:Suppose T: P2-R° is an isomorphism whose action on a basis for P2 is as follows: 1 -3 2 T(x+1)= 2 T(3x²+3x+3)=| 0 T(-x2-1) = |1 2 Find the inverse transformation T1 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 'A' character to indicate an exponent, e.g. px^2-qx+r. = (-4p-29-2r)x²+ p-+tp+q) The correct answer is: 1 T1 글기자2+(-p+r]x+(-p+q)
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