# Eigen values of a matrix depending on k

If $A = \begin{bmatrix} 2 & k \\ 0 & 1 \end{bmatrix}$. Find all values of $k$ for which A has eigenvalues 3 and -1. A has no real eigenvalues. (David Poole, Linear Algebra).

The characteristic equation $(2 - \lambda)(1 - \lambda) = 0$ doesn't depend on $k$, so is this ever true? What am I missing here?

• There might be typo in your matrix $A$; the lower left corner is $1$ and not $0$. – Dietrich Burde May 25 '16 at 11:29
• Well, that seems to be the best logical conclusion. Textbook typos hurt bad. – buzaku May 25 '16 at 11:42

The matrix you wrote down always has two eigenvalues, $2$ and $1$.