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

Question

A=[-2 a-2b+c 2a+b+c]

[2 8 a+c ]

[8 2 -4 ]

How do I find a,b, and c?

(please make your answer as detailed as possible because I find it hard to understand without details)

Thank you.

Answer 1

To be symmetric, the first row must match the first column, the second row must match the second column, and the third row must match the third column.

So, we get the following system of equations:

a - 2b + c = 2

2a + b + c = 8

a + c = 2

Since a + c = 2, c = 2-a

So, a - 2b + (2-a) = 2 and 2a + b + (2-a) = 8

-2b + 2 = 2

a + b = 6

Therefore, b = 0, a = 6, and c = -4