Question: Let A be an n n symmetric negative definite matrix. (a) What will the sign of det(A) be if n is even? If n

Let A be an n × n symmetric negative definite matrix.
(a) What will the sign of det(A) be if n is even? If n is odd?
(b) Show that the leading principal submatrices of A are negative definite.
(c) Show that the determinants of the leading principal submatrices of A alternate in sign.

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