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Question: problem 6 e we saw in the lecture that the...

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Problem 6 E) We saw in the lecture that the diagonal elements of a positive definite matrix are positive. We can generalize this further: Let A Rnxn be positive definite, and let i li,i2,...i] be a vector of pairwise different indices (ipe N, ik n). Then also the corresponding sub-matrix of A, 5 Points ainti aii2ait Ripfi.aiptp is positive definite. Explain this statement and illustrate it with examples. Notes: 1. We can use this fact to show that a matrix is not positive definite. 2. In Python, use the command numpy.outer(1,1), where i is again the index vector. 3. In Matlab, create the matrix A with the command A(1, 1), where i is the index vector. H) Show, using a method of your choice (e.g. completing the square, determinants, eigenvalues, etc.), which of the following matrices are positive definite and which are not. 1 4 -5 6 1 -3 1 0 Аз 111, A2 1-3 5-21, Аз 1 -2 1 6 2 3 100
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