Linear subspaces
23:29
Linear subspaces
Feb 20, 2011
Khan AcademySal Khan
SOLVED: A set in R2 is displayed to the right Assume the set includes the bounding lines. Give specific reason why the set H is not subspace of R2 . (For instance, find two vectors in H whose sum is not in H, or find vector in H with scalar multiple that is not in H. Draw picture:)Let and be vectors and let k be scalar: Select the correct choice below and, if necessary; fill in the answer box within your choice0A 0 B The set is not = subspace because it is The set is not : subspace because it is
SOLVED: A set in R2 is displayed to the right Assume the set includes …
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Let X be the subspace of ℝ^2 that is the union of the circles Cn of radius n and center (n, 0) for n=1,2, ⋯. Show that π1(X) is the free group *n π1(Cn), the same as for the infinite wedge sum V∞ S^1 . Show that X and V∞ S^1 are in fact homotopy equivalent, but not homeomorphic. 21. Show that the join X * Y of two nonempty spaces X and Y is simply-connected if X is path-connected. | Numerade
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