Answered: Show that p(x)=5x − 3x2 polynomial in…

Show that p(x)=5x − 3x2 polynomial in P2 vector space can be written as a linear combination of the set {3 + x2,1 − x, 1 + 3x − x2}.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Show that p(x)=5x − 3x2 polynomial in P₂ vector space can be written as a linear combination of the set {3 + x2,1 − x, 1 + 3x − x2}.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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