Given Graphs of Characteristic Polynomial of Diagonalizable Matrices, Determine the Rank of Matrices
Problem 217
Let $A, B, C$ are $2\times 2$ diagonalizable matrices.
The graphs of characteristic polynomials of $A, B, C$ are shown below. The red graph is for $A$, the blue one for $B$, and the green one for $C$.
From this information, determine the rank of the matrices $A, B,$ and $C$.
![Graphs of characteristic polynomials](https://i1.wp.com/yutsumura.com/wp-content/uploads/2016/12/graphs-of-characteristic-polynomials.jpg?resize=733%2C464)
Graphs of characteristic polynomials
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