This is a question from a linear algebra course: Let V = R[X]3, the polynomials of degree at most three, and B = {1, X, X2, X3}. Show what the image under fB is of:• the four basic elements: P1(X) = 1, P2(X) = X, P3(X) = X2 and P4(X) = X3• P(X) = 2 + 6X + 3X2 + 4X3

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 49E

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This is a question from a linear algebra course: Let V = R[X]₃, the polynomials of degree at most three, and B = {1, X, X², X³}. Show what the image under f_B is of:
• the four basic elements: P₁(X) = 1, P₂(X) = X, P₃(X) = X² and P₄(X) = X³
• P(X) = 2 + 6X + 3X² + 4X³

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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