Homework SourseIn Exercise let S be the collection of vectors x y z in R3 t
In Exercise, let S be the collection of vectors [x y z] in R^3 that satisfy the given property. In each case, either prove that S forms a subspace of R^3 or give a counterexample to show that it does not. |x - y| = |y - z|![In Exercise, let S be the collection of vectors [x y z] in R^3 that satisfy the given property. In each case, either prove that S forms a subspace of R^3 or gi](/WebImages/41/in-exercise-let-s-be-the-collection-of-vectors-x-y-z-in-r3-t-1126252-1761600591-0.webp "In Exercise, let S be the collection of vectors [x y z] in R^3 that satisfy the given property. In each case, either prove that S forms a subspace of R^3 or gi")
Solution
Consider two points in the set
(1,3,1) ,(1,3,5)
Sum of the two points must also be in the sset for it to be subspace
(1,3,1)+(1,3,5)=(2,6,6) which is not in the set.
Hence the set is not a subspace.
