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Suppose $\lambda$ is an eigenvalue of the given matrix $A$ then show that $20-\lambda$ is also an eigenvalue.

\begin{bmatrix} 40 & -29 & -11\\ -18 & 30 & -12\\ 26 & 24 & -50 \end{bmatrix}

So I observed that the columns are linearly dependent in fact $C_1+C_3=-C_2$. I am not quite sure how to proceed. I am a little unclear as to how matrix operations effect the eigenvalues. Any hints?

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Hints:

The columns are linearly dependent, therefore one of the eigenvalues is equal to _____

The sum of all eigenvalues of a matrix is equal to _____

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