4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii) W={(x,y,z)|x^2+y^2+z^2=0} iii) W={(x,y,z)|x>0}
4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii) W={(x,y,z)|x^2+y^2+z^2=0} iii) W={(x,y,z)|x>0}
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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4) Which of the following is a subspace of R^3?
Justify your answer.
i) W={(x,y,z)|x+y+z=0}
ii) W={(x,y,z)|x^2+y^2+z^2=0}
iii) W={(x,y,z)|x>0}
iv). W={(x,2x,3x)|x is a real number}
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