Answered: Consider the vector space R 4 over the…

Consider the vector space R 4 over the field of real numbers F = R 4. Let W = { ha, b, c, di | where a - 2d = 0 and a, b, c, d are real numbers } Show that W is a subspace of R * .

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 49E

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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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Consider the vector space R 4 over the field of real numbers F = R 4.
Let W = { ha, b, c, di | where a - 2d = 0 and a, b, c, d are real numbers }
Show that W is a subspace of R * .

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