The matrix $A = \begin{bmatrix}3&k\\8&8\end{bmatrix}$ has two distinct real eigenvalues iff $k > ?$
So I found the determinant by doing:
$(3 - \lambda)(8 - \lambda) - 8k = \lambda^2 - 11\lambda + 24 - 8k \implies \lambda = 8, \lambda = 3$ The thing is, I'm not really sure what they are asking me because I have found what the eigenvalues are: $\lambda_1 = 8, \lambda_2 = 3$.
I'm assuming I need to solve for $k$ somehow but it doesn't seem very straightforward to me, what am I missing here?