In Exercises 1-10, determine whether the indicated subset is a subspace of the given Euclidean space R". 1. {[r, -r] | rЄ R} in R² 3. {[n, m] | n and m are integers in R² 5. {[x, y, z] | x,y,z ER and z = 3x + 2} in R³ 7. {[x, y, z] | x,y,z Є R and z = 1, y = 2x} in R³ 9. {[2x₁, 3x2, 4x3, 5x4] | x; Є R} in R³
In Exercises 1-10, determine whether the indicated subset is a subspace of the given Euclidean space R". 1. {[r, -r] | rЄ R} in R² 3. {[n, m] | n and m are integers in R² 5. {[x, y, z] | x,y,z ER and z = 3x + 2} in R³ 7. {[x, y, z] | x,y,z Є R and z = 1, y = 2x} in R³ 9. {[2x₁, 3x2, 4x3, 5x4] | x; Є R} in R³
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 31EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set...
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