Solve the system $\displaystyle Y'=\begin{bmatrix}

1 & 3 & -3 \\

0 & 1 & 0 \\

6 & 3 & -8

\end{bmatrix}Y

$

not real sure but W|A returned this but no steps

so assume first thing we so is Eigenvalues

subtracting $\lambda$ from the diagonal entries of the given matrix and Find the determinant of the obtained matrix:

$\displaystyle \left[

\begin{array}{ccc} - \lambda+1&2&-3\\

0&-\lambda+1&0\\

6&3&-\lambda-8

\end{array} \right]

=-18\lambda

+\left(-\lambda-8\right)

\left(- \lambda + 1\right)^{2} + 18$