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Which of the following sets are subspaces of R ³? U₁ = {(x, y, z) = R ³ | x+y=z=0} U₂ = {(x, y, xy) | x, y ≤ R} U3 = {(x, y, z) = R ³ | x(y - z)=0} U₁ = {s(1,0,0) + t(0,0,1) | s,t = R} U5 {t(1,2,3) | t ≤ R} = U6 = {(m, m, 2m) | m = ....., -2,-1,0, 1, 2,...} Enter a list of numbers corresponding to subspaces, separated by semicolons. For example, if only U₁ and U₂ are subspaces, then you would enter 1:2

Which of the following sets are subspaces of R ³? U₁ = {(x, y, z) = R ³ | x+y=z=0} U₂ = {(x, y, xy) | x, y ≤ R} U3 = {(x, y, z) = R ³ | x(y - z)=0} U₁ = {s(1,0,0) + t(0,0,1) | s,t = R} U5 {t(1,2,3) | t ≤ R} = U6 = {(m, m, 2m) | m = ....., -2,-1,0, 1, 2,...} Enter a list of numbers corresponding to subspaces, separated by semicolons. For example, if only U₁ and U₂ are subspaces, then you would enter 1:2

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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Which of the following sets are subspaces of R ³? U₁ = {(x, y, z) = R ³ | x+y=z=0} U₂ = {(x, y, xy) | x, y ≤ R} U3 = {(x, y, z) = R ³ | x(y - z)=0} U₁ = {s(1,0,0) + t(0,0,1) | s,t = R} U5 {t(1,2,3) | t ≤ R} -= U6 = {(m, m, 2m) | m = ' , -2,-1, 0, 1, 2,...} Enter a list of numbers corresponding to subspaces, separated by semicolons. For example, if only U₁ and U₂ are subspaces, then you would enter 1:2
Transcribed Image Text:Which of the following sets are subspaces of R ³? U₁ = {(x, y, z) = R ³ | x+y=z=0} U₂ = {(x, y, xy) | x, y ≤ R} U3 = {(x, y, z) = R ³ | x(y - z)=0} U₁ = {s(1,0,0) + t(0,0,1) | s,t = R} U5 {t(1,2,3) | t ≤ R} -= U6 = {(m, m, 2m) | m = ' , -2,-1, 0, 1, 2,...} Enter a list of numbers corresponding to subspaces, separated by semicolons. For example, if only U₁ and U₂ are subspaces, then you would enter 1:2
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