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:
\(\displaystyle \left[
\begin{array}{ccc} - \lambda+1&2&-3\\
0&-\lambda+1&0\\
6&3&-\lambda-8
\end{array} \right]
=-18\lambda
+\left(-\lambda-8\right)
\left(- \lambda + 1\right)^{2} + 18\)

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:
\(\displaystyle \left[
\begin{array}{ccc} - \lambda+1&2&-3\\
0&-\lambda+1&0\\
6&3&-\lambda-8
\end{array} \right]
=-18\lambda
+\left(-\lambda-8\right)
\left(- \lambda + 1\right)^{2} + 18\)

Last edited: