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Assume that A and B are two symmetric k x k matrices.
a) Show that AB = (BA)^T
b) Show that if A is invertible, then A^-1 is also a symmetric matrix.
c) Assume that we can write
A= [ A_1 A_2 ]
With A_1 a 2 x 2, A_2 an m x 3, A_3 a 3 x n and A_4 a p x q matrix. What can we say about m, n, p, q? Which of the four submatrices is symmetric? Can you say anything about the relationship between A_2 and A_3?© BrainMass Inc. brainmass.com March 5, 2021, 12:38 am ad1c9bdddf
This solution provides a detailed, step-by-step explanation of the given linear algebra problem.