linear algebra (7) Let T : P2 → P2 be defined by T(p(x)) =p(x) = 3+1+ 4r², then T(p(t)) = p(0) + p(1)t = (3+0+4- 0²) + (3 +1+4.12)t = 3+ 8t.) Let a = {1,x – 1,r² – 1} and B = {1,1,r²} be twobases of P2.(a) Find the a-matrix and B-matrix of T.(b) Find the change of basis matrix S3 ra.(c) What is the relation of the three matrices you have found? Are anytwo of them similar? (Recall that similar has a technical meaningherep(0) + p(1)r. (For example, ifsee Definition 3.4.5.)

Every linear map correspond to a matrix and the matrix can be determined with the help of basis and…

Answered: 7) Let T : P2 → P2 be defined by…

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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linear algebra

(7) Let T : P2 → P2 be defined by T(p(x)) =
p(x) = 3+1+ 4r², then T(p(t)) = p(0) + p(1)t = (3+0+4- 0²) + (3 +
1+4.12)t = 3+ 8t.) Let a = {1,x – 1,r² – 1} and B = {1,1,r²} be two
bases of P2.
(a) Find the a-matrix and B-matrix of T.
(b) Find the change of basis matrix S3 ra.
(c) What is the relation of the three matrices you have found? Are any
two of them similar? (Recall that similar has a technical meaning
here
p(0) + p(1)r. (For example, if
see Definition 3.4.5.)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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