Apply the eigenvalue method to find a general solution to:

x1' = x1 + 2x2 + 2x3

x2' = 2x1 + 7x2 + x3

x3' = 2x1 + x2 + 7x3

Here's what Ive done:

The matrix form of the system is:

x' = 1 2 2

.......2 7 1

.......2 1 7

Then the book says to do this:

A - &I = 1-&....2......2

..............2....7-&....1

..............2.....1.....7-&

I can't follow the rest. Can someone show how to do the rest? Thanks