Hi, please help with this Linear Algebra question, please! Thank you! Let T : R³ → V and U : V → P2 (R) be lineartransformations, where V is a 2-dimensional vectorspace. Suppose that12(T = (;1 01[Uand1-1||112where a is the standard ordered basis for R3, B isan unknown basis for V, andY = {1, 1+ x, 1+ x + x² }. Given thatUT(1, 1, 1) = a + bæ + cx²,find the value of the number a.

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Description: Hi, please help with this Linear Algebra question, please! Thank you! Let T : R³ → V and U : V → P2 (R) be lineartransformations, where V is a 2-dimensional vectorspace. Suppose that12(T = (;1 01[Uand1-1||112where a is the standard ordered basis for

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Answered: Let T : R³ → V and U : V → P2 (R) be…

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, please help with this Linear Algebra question, please! Thank you!

Let T : R³ → V and U : V → P2 (R) be linear
transformations, where V is a 2-dimensional vector
space. Suppose that
1
2
(T = (;
1 0
1
[U
and
1
-1
||
1
1
2
where a is the standard ordered basis for R3, B is
an unknown basis for V, and
Y = {1, 1+ x, 1+ x + x² }. Given that
UT(1, 1, 1) = a + bæ + cx²,
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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