Eigen do this one!

Algebra Level 2

Let \(A\) be the matrix \( A = \begin{pmatrix} 3 & 5 \\ 1 & 7 \\ \end{pmatrix} \). An eigenvalue of \(A\) is a real number \(\lambda\) such that there exists a non-zero vector \({x_\lambda} = \begin{pmatrix} X \\ Y \end{pmatrix} \) such that \(Ax_\lambda=\lambda x_\lambda\). What is the sum of all the eigenvalues of \(A\) (i.e. sum of all the possible \(\lambda\))?

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