Answered: Let S be the set of all elements of the…

Let S be the set of all elements of the form (x + 2y , y ,-x + 3y) in R^3, where x,y ∈ R. Show that S is a subspace of〖 R〗^3.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 60CR: Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.

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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.

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Let S be the set of all elements of the form (x + 2y , y ,-x + 3y) in R^3, where x,y ∈ R. Show that S is a subspace of〖 R〗^3.

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