Question: Let A = C d The quantity a + d (i.e. the sum of the entries in the lead diagonal of A) is call the

Let A = C d The quantity a + d (i.e. the sum of the entries in the lead diagonal of A) is

distinct) eigenvalues. Prove the following.(a) The trace of A is the sum

Let A = C d The quantity a + d (i.e. the sum of the entries in the lead diagonal of A) is call the trace of A. Suppose A has 2 real (not necessarily distinct) eigenvalues. Prove the following.(a) The trace of A is the sum of the eigenvalues of A. (b) The eigenvalues of A and AT are the same. (c) If A does not have 0 as an eigenvalue then the eigenvalues of A\" are the reciprocal of the eigenvalues of At

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