To do this, we need to solve the characteristic equation:
$$\det(A-\lambda I) = 0$$
where $A$ is the matrix and $I$ is the identity matrix. Substituting the values from the given matrix, we get:
$$\begin{vmatrix}2-\lambda & -3 & 4 \\-3 & 2-\lambda & 0 \\4 & 0 &
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