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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