First, we need to find the eigenvalues and eigenvectors of the coefficient matrix A = [[6, -8], [-12, 0]].
The characteristic equation is det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.
det([[6, -8], [-12, 0]] - λ[[1, 0], [0, 1]]) = 0
=>
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