Suppose T: P3-M2,2 is an isomorphism whose action is defined byT(ax³ + bx²+cx+d)=b+c=2d b-2da+b b+c-4dand that we have the ordered bases= 1x³, x²B =X,for P3 and M₂.2 respectively.MDB(T)a) Find the matrix of I corresponding to the ordered bases B and D.00000000010 0100¹ D- [8] [8] [8] 8:][0].1="00 0010b) Find the matrix of I-1 corresponding to the ordered bases D and B.000MBD(T¹)= 0 0 0000T¹2²:0= 0r sc) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants.Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.

Answered: Suppose T: P3-M2,2 is an isomorphism…

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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8-3) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2,... are not vectors but are entries in vectors a) T(x1, x2) = (2x2-3x1, x1-4x2, 0, x2) b) T(x1, x2, x3, x4) = 2x1 + 3x - 4x4 (T:R* → R)
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