Question: 2. Consider the following block matrix: M = (1) where N is a m x m real symmetric matrix, a is a m-dimensional real vector,

2. Consider the following block matrix: M = (1) where N is a m x m real symmetric matrix, a is a m-dimensional real vector, and c is a real scalar. 1) (30 points) Prove that the following two statements are equivalent. i) M is a positive semidefinite (PSD) matrix. ii) There is a m-dimensional vector b which satisfies a = Nb and c 2 b Nb; and N is PSD

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