Answered: Suppose W1 and W2 are subspaces of a…

Suppose W1 and W2 are subspaces of a vector space, V. Define W as follows: W = {w1 + W2 | W1 E W1 and w2 E W2} Prove that W is a subspace of V.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 30EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1

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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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Suppose W1 and W2 are subspaces of a vector space, V. Define W as follows:
W
= {w1 + W2 | W1 E W1 and w2 E W2}
Prove that W is a subspace of V.

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