- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem!
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!
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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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Remember to read the POTW submission guidelines to find out how to submit your answers!