Symmetric Matrices

Date: 10/27/1999 at 10:07:54
From: Marnie
Subject: Symmetric matrices

I have tried looking at the local library and have read different 
books, but I really need some good hints on how to solve this problem:

Find all values of a, b, and c for which A is symmetric:

         [2  a-2b+2c  2a+b+c]
     A = [3     5       a+c ]
         [0    -2        7  ]

Thank you.

Date: 10/27/1999 at 11:04:30
From: Doctor Hans
Subject: Re: Symmetric matrices

Hi Marnie,

Let me give you a hint. You seem to be unsure of what it means that a 
matrix is symmetric. It simply means that entry (i,j) equals entry 
(j,i) for all i and j.

In your case we have (note that the diagonal entries are not that 
interesting in this context):

     entries (1,2) and (2,1) are equal: (a-2b+2c) =  3
     entries (1,3) and (3,1) are equal:  (2a+b+c) =  0
     entries (2,3) and (3,2) are equal:     (a+c) = -2

So now you have three equations in three variables. What is left for 
you to do is to solve them, and you will have your answer.

Sincerely,

- Doctor Hans, The Math Forum
  http://mathforum.org/dr.math/