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**[SOLVED] Positive Definite Matrices**

a) If A is Symmetric show that A-λI is positive definite if and only if all eigenvalues of A are >λ, and A-λI is negative definite if and only if all eigenvalues of A are <λ.

b) Use this result to show that all the eigenvalues of

[ 5 2 -1 0]

[ 2 5 0 1]

[-1 0 5 -2]

[ 0 1 -2 5]

are between zero and eight.