The sum of Eigen values of matrix, [M] is where \[\left[ {\text{M}} \right] = \left[ {\begin{array}{*{20}{c}} {215}&{650}&{795} \\ {655}&{150}&{835} \\ {485}&{355}&{550} \end{array}} \right]\] A. 915 B. 1355 C. 1640 D. 2180

The sum of the eigenvalues of a matrix is equal to the trace of the matrix. The trace of a matrix is the sum of the elements on the main diagonal. In this case, the matrix is $\left[ {\text{M}} \right] = \left[ {\begin{array}{*{20}{c}} {215}&{650}&{795} \ {655}&{150}&{835} \ {485}&{355}&{550} \end{array}} \right]$. The trace of this matrix is $215 + 150 + 550 = 915$. Therefore, the sum of the eigenvalues of this matrix is $\boxed{915}$.

Here is a brief explanation of each option:

• Option A: $915$ is the correct answer.
• Option B: $1355$ is the sum of the elements on the first and third rows of the matrix. However, the sum of the eigenvalues is not equal to the sum of the elements on any row or column of the matrix.
• Option C: $1640$ is the sum of the elements on the main diagonal of the matrix. However, the sum of the eigenvalues is not equal to the sum of the elements on the main diagonal.
• Option D: $2180$ is the sum of the squares of the elements on the main diagonal of the matrix. However, the sum of the eigenvalues is not equal to the sum of the squares of the elements on the main diagonal.