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Question: 5 show that for a symmetric matrix w e rnxn...

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5. Show that for a symmetric matrix W E Rnxn and a diagonal matrix D defined by Dii-Xwij, if Wj 20 for al 1 i,j S n, then L D - W (which is called the Laplacian matrix) is positive semidefinite, and has an eigenvector of [1,1,... ,1],

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