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Suppose A is a 100×100 real symmetric matrix whose diagonal entries are all positive.Then which of the following is necessarily true?

a)all eigenvalues of A are greater than 0

b)no eigenvalue of A is greater than 0

c)at least one eigenvalue of A is greater than 0

d)none of these

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Given: A is 100*100 symmetric matrix with all diagonal entries >0, which would imply that the matrix A is a positive definite symmetric matrix.

And, for a positive definite matrix we know that all eigen values >0.

Option a) is correct.

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