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The sum of the eigenvalues of the matrix \(M\), where \[ M=\begin{bmatrix} 215 & 650 & 795\\ 655 & 150 & 835\\ 485 & 355 & 550 \end{bmatrix} \] is

1. 915
2. 1355
3. 1640
4. 2180

Correct answer: 915

Solution

The sum of eigenvalues of a square matrix equals its trace, i.e., the sum of diagonal elements. Here the trace is \(215+150+550=915\). Therefore, the sum of eigenvalues is 915.

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