Hi, I need help with this Linear Algebra exercise, please. Thank you! Let 3 the the standard ordered basis on M2×2(R), lety = {1 – x, 1+ x}, and letT: M2x2 (R) –→ P1 (R) be the linear transformation%3D1 20 -1such that TGiven that3 1 -4TG) --1= a + bx,1-1 -1find the value of the number a.

Name: Hi, I need help with this Linear Algebra exercise, please. Thank you!
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Description: Hi, I need help with this Linear Algebra exercise, please. Thank you! Let 3 the the standard ordered basis on M2×2(R), lety = {1 – x, 1+ x}, and letT: M2x2 (R) –→ P1 (R) be the linear transformation%3D1 20 -1such that TGiven that3 1 -4TG) --1= a + bx

a = 10 b = 2 The detailed solution is as follows below:

Answered: Let 3 the the standard ordered basis on…

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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Hi, I need help with this Linear Algebra exercise, please. Thank you!

Let 3 the the standard ordered basis on M2×2(R), let
y = {1 – x, 1+ x}, and let
T: M2x2 (R) –→ P1 (R) be the linear transformation
%3D
1 2
0 -1
such that T
Given that
3 1 -4
TG) --
1
= a + bx,
1
-1 -1
find the value of the number a.

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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