Question

The matrix A= {8,k},{-2,2} has two distinct real eigenvalues if and only if k<

Answer 1

So, any ideas?

Answer 2

Do you know how to find eigen values? Well try to find them.

Answer 3

You should end up with a quadratic equation. Then look at the discriminant, which is \(b^2-4ac\).

Answer 4

We know from before that \(a=1\), \(b\) is the trace, and \(c\) is the determinant.

Answer 5

For two distinct values you want \(b^2-ac > 0\). If it is \(0\) they are not distinct (repeated eigen values). If it is \(<0\), then they are complex.