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In Exercises 9-17, W is a subset of R^3 consisting of vectors of the form x = [ x1 x2 x3 ]. In each case, determine whether W is a subspace of R^3. If W is a subspace, then give a geometric description of W. 9. W = {x: x3 = 2x1 - x2} 10. W = {x: x2 = x3 + x1} 11. W = {x: x1x2 = x3} 12. W = {x: x1 = 2x3} 13. W = {x: x1^2 = x1 + x2} 14. W = {x: x2 = 0} 15. W = {x: x1 = 2x3, x2 = -x3} 16. W = {x: x3 = x2 = 2x1} 17. W = {x: x2 = x3 = 0} 18. Let a be a fixed vector in R^3, and define W to be the

          In Exercises 9-17, W is a subset of R^3 consisting of vectors of the form
x = [
x1
x2
x3
].
In each case, determine whether W is a subspace of R^3. If W is a subspace, then give a geometric description of W.
9. W = {x: x3 = 2x1 - x2}
10. W = {x: x2 = x3 + x1}
11. W = {x: x1x2 = x3}
12. W = {x: x1 = 2x3}
13. W = {x: x1^2 = x1 + x2}
14. W = {x: x2 = 0}
15. W = {x: x1 = 2x3, x2 = -x3}
16. W = {x: x3 = x2 = 2x1}
17. W = {x: x2 = x3 = 0}
18. Let a be a fixed vector in R^3, and define W to be the

In Exercises 9-17, W is a subset of R^3 consisting of vectors of the form
x = [
x1
x2
x3
].
In each case, determine whether W is a subspace of R^3. If W is a subspace, then give a geometric description of W.
9. W = x: x3 = 2x1 - x2
10. W = x: x2 = x3 + x1
11. W = x: x1x2 = x3
12. W = x: x1 = 2x3
13. W = x: x1^2 = x1 + x2
14. W = x: x2 = 0
15. W = x: x1 = 2x3, x2 = -x3
16. W = x: x3 = x2 = 2x1
17. W = x: x2 = x3 = 0
18. Let a be a fixed vector in R^3, and define W to be the

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Calculus: Early Transcendentals

James Stewart 8th Edition

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10/18/2022

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In Exercises 9-17, W is a subset of R^3 consisting of vectors of the form x = [x1; x2; x3]. In each case, determine whether W is a subspace of R^3. If W is a subspace, then give a geometric description of W. 9. W = {x: x3 = 2x1 - x2} 10. W = {x: x2 = x3 + x1} 11. W = {x: x1x2 = x3} 12. W = {x: x1 = 2x3} 13. W = {x: x1^2 = x1 + x2} 14. W = {x: x2 = 0} 15. W = {x: x1 = 2x3, x2 = -x3} 16. W = {x: x3 = x2 = 2x1} 17. W = {x: x2 = x3 = 0} 18. Let a be a fixed vector in R^3, and define W to be the...