# Characteristic Polynomial Calculator

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

## Your Input

**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).

## Answer

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