Next thing to do is solve
Then follow the rest of this example
Pauls Online Notes : Differential Equations - Real Eigenvalues
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
Next thing to do is solve
Then follow the rest of this example
Pauls Online Notes : Differential Equations - Real Eigenvalues
Ok I get 3 eigenvalues: 0,6,9
Case 1:
I plug 0 into the matrix from the original post and notcie that its a singular matrix b/c the det is 0. In a 2x2 matrix, this means I can arbitrary choose a and solve for b. How does this work for my 3x3 matrix? Thanks