Determine whether the following sets form sub- spaces of R³: (a) {(x1,x2, X3)" | x1 +x3 = 1} (b) {(x1, X2, x3)" | x1 = x2 = x3} (c) {(x1, x2, X3)" | x3 = x1 +x2} (d) {(x1, X2, X3)" | X3 = x1 or x3 = x2}

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 62E
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Determine whether the following sets form sub-
spaces of R³:
(a) {(x1,X2, X3)" | x1 + x3 = 1}
(b) {(x1, x2, X3)" | x1 = x2 = x3}
(c) {(x1, X2, X3)" | X3 = x1 + x2}
(d) {(x1, X2, X3)" | X3 = x1 or x3 = X2}
Transcribed Image Text:Determine whether the following sets form sub- spaces of R³: (a) {(x1,X2, X3)" | x1 + x3 = 1} (b) {(x1, x2, X3)" | x1 = x2 = x3} (c) {(x1, X2, X3)" | X3 = x1 + x2} (d) {(x1, X2, X3)" | X3 = x1 or x3 = X2}
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