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Define the subset V, of R3 to be the set of all vectors in R³ satisfying x+y+z = r, where r is a real number. Determine all values of r for which V, is a subspace of R³. Justify your answer.

Define the subset V, of R3 to be the set of all vectors in R³ satisfying x+y+z = r, where r is a real number. Determine all values of r for which V, is a subspace of R³. Justify your answer.

Linear Algebra: A Modern Introduction
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 34EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
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Define the subset V, of R3 to be the set of all vectors y in R satisfying x +y+z = r, where r is a real number. Determine all values of r for which V, is a subspace of R³. Justify your answer.
Transcribed Image Text:Define the subset V, of R3 to be the set of all vectors y in R satisfying x +y+z = r, where r is a real number. Determine all values of r for which V, is a subspace of R³. Justify your answer.
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