# Characteristic Polynomial Calculator

The calculator will find the characteristic polynomial of the given matrix, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the characteristic polynomial of $\left[\begin{array}{cc}2 & 1\\5 & 5\end{array}\right]$.

## Solution

Start from forming a new matrix by subtracting $\lambda$ from the diagonal entries of the given matrix:

$\left[\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right]$

The characteristic polynomial is the determinant of the obtained matrix:

$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \lambda^{2} - 7 \lambda + 5$ (for steps, see determinant calculator).

The characteristic polynomial is $p{\left(\lambda \right)} = \lambda^{2} - 7 \lambda + 5$A.