Can I perform elementary line operations to $\det(A-\lambda I)$ like this?

286 Views Asked by At

I have a $4 \times 4$ matrix:

$$A = \begin{pmatrix} 2 & 3 & 1 & 0 \\ 4 & -2 & 0 & -3\\ 8 & -1 & 2 & 1\\ 1 & 0 & 3 & 4\\ \end{pmatrix}$$

I want to find the eigenvalues so I have to solve $\det(A - \lambda I)$. Can I perform line operations to $A$ before I subtract its diagonal with $\lambda$?

Is there any good online calculator that shows the steps of finding the determinant, eigenvalues etc?

Thanks in advance!