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In Exercises 1-10, determine wheth indicated subset is a subspace of the Euclidean space R". 1. {[r, -r] | rE R} in R² 2. {[x, x + 1] x ER} in R² 3. {[n, m] | n and m are integers} 4. {[x, y] | x,y E R and x,y ≥ 0} quadrant of R²) 5. {[x, y, z] | x,y,z ER and z = 3 6. {[x, y, z] | x,y,z E R and x = 2 7. {[x, y, z] | x,y,z E R and z = 1 8. {[2x, x + y, y] | x,y = R} in R³

In Exercises 1-10, determine wheth indicated subset is a subspace of the Euclidean space R". 1. {[r, -r] | rE R} in R² 2. {[x, x + 1] x ER} in R² 3. {[n, m] | n and m are integers} 4. {[x, y] | x,y E R and x,y ≥ 0} quadrant of R²) 5. {[x, y, z] | x,y,z ER and z = 3 6. {[x, y, z] | x,y,z E R and x = 2 7. {[x, y, z] | x,y,z E R and z = 1 8. {[2x, x + y, y] | x,y = R} in R³

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For Numbers 4 and 6.

Determine whether the indicated subset is a subspace of the given Euclidean space Rn.

In Exercises 1-10, determine whether the indicated subset is a subspace of the given Euclidean space R". 1. {[r, -r] | r ER} in R2 2. {[x, x + 1] | x ER} in R² 3. {[n, m] | n and m are integers} in R² 4. {[x, y] | x,y ER and x,y ≥ 0} (the first quadrant of R²) 5. {[x, y, z] | x,y,z E R and z = 3x + 2} in R³ 6. {[x, y, z] | x,y,z E R and x = 2y + z} in R³ 7. {[x, y, z] | x,y,z E R and z = 1, y = 2x} in R³ 8. {[2x, x + y, y] | x,y = R} in R³ E
Transcribed Image Text:In Exercises 1-10, determine whether the indicated subset is a subspace of the given Euclidean space R". 1. {[r, -r] | r ER} in R2 2. {[x, x + 1] | x ER} in R² 3. {[n, m] | n and m are integers} in R² 4. {[x, y] | x,y ER and x,y ≥ 0} (the first quadrant of R²) 5. {[x, y, z] | x,y,z E R and z = 3x + 2} in R³ 6. {[x, y, z] | x,y,z E R and x = 2y + z} in R³ 7. {[x, y, z] | x,y,z E R and z = 1, y = 2x} in R³ 8. {[2x, x + y, y] | x,y = R} in R³ E
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