I know how to compute the eigenvectors given the matrix and then finding eigenvalues. I could turn A into a triangular matrix and then compute for lambdas, but I wanted to know if there was another procedure by using the eigenvectors and A to find the eigenvalues.
Any help is appreciated.
Thanks!
Best Answer
$$ \begin{bmatrix} 13 & 2 & -18\\ 14 & 1 & -18\\ 10 & 2 & -15 \end{bmatrix}\cdot \begin{bmatrix} -1\\ -1\\ -1 \end{bmatrix}= \begin{bmatrix} 3\\ 3\\ 3 \end{bmatrix}=-3\cdot \begin{bmatrix} -1\\ -1\\ -1 \end{bmatrix}. $$
Thus, $-3$ is an eigenvalue of $A$. Try the same strategy for the other two eigenvectors.