Explore BrainMass

# Linear Algebra Question: Matrices and Symmetry

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for full details.

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 ]
A_3 A_4

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
https://brainmass.com/math/linear-algebra/linear-algebra-question-matrices-symmetry-522483

#### Solution Summary

This solution provides a detailed, step-by-step explanation of the given linear algebra problem.

\$2.49