Suppose T: P3→M2.2 is an isomorphism whose action is defined by3a-3c -b-3cT(ax³ + bx²+cx+d)=-3c+d -b-3c+dand that we have the ordered bases=√x³, x²,3B =for P3 and M2,2 respectively.a) Find the matrix of I corresponding to the ordered bases B and D.000MDB(T) 0 0 0000MBD(T-1):X ,=b) Find the matrix of T-1 corresponding to the ordered bases D and B.T-1p q-0011 D=¹ D- [10] - [ 1 ] - [ ] [ ]"00 0001c) Describe the action of I-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.r s000000000

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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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Which of the following six sets are subrings of M(R)? Which ones have an identity? 0 0 (a) All matrices of the form (8 5) with reQ. (b) All matrices of the form (c) All matrices of the form (d) All matrices of the form (a b) 0 Ca a a with a, b, cЄZ. b with a, b, c = R. 0 with a Є R. 0 with a ЄR. (e) All matrices of the form a (69) (f) All matrices of the form 0 (a) with a ЄR. 0
-9 V₁ = --[-] and X₂ such that T(x) is Ax for each x. Let x = A = X₁ -2 [3] and let T: R² R² be a linear transformation that maps x into x₁v₁ +X₂V₂. Find a matrix A -8 and V₂ =
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