Question: (a) Show that every diagonal entry of a positive definite matrix must be positive. (b) Write down a symmetric matrix with all positive diagonal entries

(a) Show that every diagonal entry of a positive definite matrix must be positive.
(b) Write down a symmetric matrix with all positive diagonal entries that is not positive definite.
(c) Find a nonzero matrix with one or more zero diagonal entries that is positive semi-definite.

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