Answer
See solution
Work Step by Step
Let A be a lower triangular matrix of the form $\begin{bmatrix}
a_{11}&0&0\\a_{21}&a_{22}&0\\a_{31}&a_{32}&a_{33}
\end{bmatrix}$.
As shown in exercise 27, the eigenvalues of A must be equal to the eigenvalues of the transpose of A, shown below.
$\begin{bmatrix}
a_{11}&a_{21}&a_{31}\\0&a_{22}&a_{32}\\0&0&a_{33}
\end{bmatrix}$. Thus the matrix now has the same form as the one in theorem 1, showing that it is true for lower triangular matrices.
