We are given a non-linear system:
$4x_1 − x_2 + x_3 = x_1x_4,$
$−x_1 + 3x_2 − 2x_3 = x_2x_4$
$x_1 − 2x_2 + 3x_3 = x_3x_4$
$x_1^2 + x_2^2 + x_3^2 = 1$
And the question asks: Show how to solve the nonlinear system via the computation of all the eigenvalues and eigenvectors of a 3 × 3 matrix
It is likely the question asks for a numerical method.
If you can provide some hint beofore 8am, PST, I would really appreciate it:)