I have a problem with determining eigenvalues. This is what I've got thus far:
Identify and sketch the graph of the quadratic equation
4x² + 10xy + 4y² = 9
This gives the matrix form:
Now we find the eigenvalues:
Det(A – xI) =
= x² – 8x – 9
= (x – 9)(x + 1)
From there, it's pretty simple solving:
My problem here is: How do I know which eigenvalue is which? It obviously makes quite a bit of difference to the final result. Nothing in my textbook says.
Since are eigenvalues, we find their corresponding eigenvectors. If we do so, we can choose where the indices correspond. Now form the matrix using , i.e., . Let , so . Any solution satisfies the equation . Note that , so . So solutions correspond to solutions of , i.e., the equation , via the transformation .
Hope this helps.
where a,b,c,d are
I should explain more:
once the equation
has been reached, I need to state what graphic function it is and plot the graph. So it would appear that knowing what and are important as I get either
which lead to vastly different graphs. As I said, there's nothing mentioned in my lecture notes about this, and because I'm doing this paper by correspondence I can't go speak to the lecturer.