1. ## Did I get the right answer? [matrix symmetry]

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

I set this matrix equal to its transpose and used them both to make the following system of equations, and solved it by gaussian elimination

a - 2b + 2c = 3
2a + b + c = 0
a + c = -2

I got a = -18, b = 5, c = 31

How can I check if this is the right answer?

2. Originally Posted by Hasan1

I got a = -18, b = 5, c = 31

How can I check if this is the right answer?
Substitute these values back into A. If A is then symmetric the solution set is correct.

3. What if it is the case that the solution set is correct but there are no such values a,b,c that will make A symmetric?

4. Originally Posted by Hasan1
What if it is the case that the solution set is correct but there are no such values a,b,c that will make A symmetric?
What? You are asking "what if these numbers make A symmetric but there are no numbers that make A symmetric?" !!!! That's impossible.

In any case, these numbers are NOT correct because
-18- 2(5)+ 3(31)= -18- 10+ 93= -28+ 93= 55, not 3