Question: (a) Prove that a positive definite matrix has positive determinant: det K > 0. (b) Show that a positive definite matrix has positive trace: tr

(a) Prove that a positive definite matrix has positive determinant: det K > 0.
(b) Show that a positive definite matrix has positive trace: tr K >0.
(c) Show that every 2 x 2 symmetric matrix with positive determinant and positive trace is positive definite.
(d) Find a symmetric 3 x 3 matrix with positive determinant and positive trace that is not positive definite.

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a According to Theorem 152 det K is equal to the product of its pivots which ... View full answer

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