Symmetric MatricesDate: 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/ |
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