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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}

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}

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Question: 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}
Transcribed Image Text:Question: 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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