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Consider the vector space R3 with the usual operations of vector addition and scalar multiplication. Which of the following subsets of R3 is a subspace of R3? {(а, b, с)| а + b +с %3D 0} O {(a, b, c)| a + b+c = 1} O {(a, b, c)| a > 0} O {(a, b, c)| a < b}

Consider the vector space R3 with the usual operations of vector addition and scalar multiplication. Which of the following subsets of R3 is a subspace of R3? {(а, b, с)| а + b +с %3D 0} O {(a, b, c)| a + b+c = 1} O {(a, b, c)| a > 0} O {(a, b, c)| a < b}

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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Please explain thoroughly why the 1st choice is the correct answer. Thank you

Consider the vector space R3 with the usual operations of vector addition and scalar multiplication. Which of the following subsets of R3 is a subspace of R3? {(а, b, с)| а + b +с %3D 0} O {(a, b, c)| a + b+c = 1} O {(a, b, c)| a > 0} O {(a, b, c)| a < b}
Transcribed Image Text:Consider the vector space R3 with the usual operations of vector addition and scalar multiplication. Which of the following subsets of R3 is a subspace of R3? {(а, b, с)| а + b +с %3D 0} O {(a, b, c)| a + b+c = 1} O {(a, b, c)| a > 0} O {(a, b, c)| a < b}
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