Q3. (25 pts) Let V be a vector space over a field F and X, Y subspaces of V. Is XUY a subspace of V? If yes, prove your argument. If no, give a counter example and then write a proposition which gives necessary and sufficient condition () so that XUY is a subspace of V. Then prove your proposition.

Q3. (25 pts) Let V be a vector space over a field F and X, Y subspaces of V. Is XUY a subspace of V? If yes, prove your argument. If no, give a counter example and then write a proposition which gives necessary and sufficient condition () so that XUY is a subspace of V. Then prove your proposition.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 44EQ

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Concept explainers

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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Q3. (25 pts) Let V be a vector space over a field F and X,Y subspaces of V. Is XUY
a subspace of V? If yes, prove your argument. If no, give a counter example and then
write a proposition which gives necessary and sufficient condition () so that XUY is
a subspace of V. Then prove your proposition.

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