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Q30Section B (Part B)30 of 120

Largest eigenvalue of a matrix with equal row sums

Consider the real matrix

A=(29055171284626171333382167013).A=\begin{pmatrix}29&0&55&17\\1&28&46&26\\17&13&33&38\\21&67&0&13\end{pmatrix}.

What is the largest real eigenvalue of AA?

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