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## Homework Statement

For what ##h## is the matrix ##\begin{bmatrix}1 & -h^2 & 2h \\ 0 & 2h & h \\ 0 & 0 & h^2 \end{bmatrix}## diagonalizable with real eigenvalues? (More than one may be correct)

a) -2, b) -1, c) 0, d) 1, e) 2

## Homework Equations

## The Attempt at a Solution

We already know the eigenvalues, since the matrix is upper triangular. How do we proceed? Do we just plug in the values of h and see if it is diagonalizable? It seems like that would take a very long time...