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- #1

- Jan 26, 2012

- 995

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**Problem**: Let $A$ be the matrix given by

\[A = \begin{pmatrix} a & b \\ c & d\end{pmatrix}.\]

Prove that the characteristic polynomial $p(\lambda)$ of $A$ is given by

\[p(\lambda) = \lambda^2 - \text{tr}(A)\lambda + \det(A),\]

where $\text{tr}(A)$ denotes the trace of the matrix $A$.

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