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There are 7000 undergraduate students at Stanford. Let M be the 7000 × 7000 matrix whose i j entry is 1 if student i and student j are Facebook friends and 0 if they are not.

There are 7000 undergraduate students at Stanford. Let M be the 7000 × 7000 matrix whose i j entry is 1 if student i and student j are Facebook friends and 0 if they are not. (Here we assume that Facebook does not permit a person to be a friend of themselves, so all the diagonal entries of M are zero.) Let u be the vector in R7000 each of whose entries equals 1. What does the vector Mu represent?
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