Which of the following sets are vector subspaces of R3 and why? i. S1 ={x in R3: x1 + x2 = 0, x1 + x3 = 0} ii. S2 ={x in R3: x1 + x2 − x3 = 0} iii. S3 ={x in R3: x3 ≥ 0} iv. S4 ={x in R3: x3 = 0}
Which of the following sets are vector subspaces of R3 and why? i. S1 ={x in R3: x1 + x2 = 0, x1 + x3 = 0} ii. S2 ={x in R3: x1 + x2 − x3 = 0} iii. S3 ={x in R3: x3 ≥ 0} iv. S4 ={x in R3: x3 = 0}
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 23CM
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Which of the following sets are
i. S1 ={x in R3: x1 + x2 = 0, x1 + x3 = 0}
ii. S2 ={x in R3: x1 + x2 − x3 = 0}
iii. S3 ={x in R3: x3 ≥ 0}
iv. S4 ={x in R3: x3 = 0}
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