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**Unformatted text preview: **assume that they cancel each other out.) Let v ( n ) be the vector in R 2 whose i-th entry is the number of birds on island i in the year n . 1. Find a matrix A so that v ( n + 1) = A v ( n ) 2. Find all vectors v in R 2 such that A v = v . What is the signiﬁcance of such a vector v in terms of bird relocations? E3. There are 6000 undergraduate students at Stanford. Let M be the 6000 × 6000 matrix whose ij entry is 1 if student i and student j have met each other and 0 if they have not met. What information does M 2 contain? That is, what is the meaning of the ij entry of M 2 ? 1...

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