(a) Construct the incidence matrix A for the disconnected digraph D in the figure. (b) Verify that...
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(b) Verify that dim ker A = 3, which is the same as the number of connected components, meaning the maximal connected subgraphs in D.
(c) Can you assign an interpretation to your basis for ker A ?
(d) Try proving the general statement that dim ker A equals the number of connected components in the digraph D.
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a b The vectors form a basis for ker A c The entries of each vi are indexed by the vertices Thus the ...View the full answer
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