# Characteristic Polynomial Calculator

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

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