Find the general solution of the given system. dx dt = 3x − y − z dy dt = x + y − z dz dt = x − y + z x(t), y(t), z(t) =

In matrix from, the system is

The coefficient matrix has eigenvalues such that

(where the subscript denotes multiplicity of the eigenvalue).

:

By picking , we can then set and , and vice versa, to find two corresponding eigenvectors,

:

We obtain independent of by picking , so that the third corresponding eigenvector is

Then the general solution to this system is

its the fourth option

true

step-by-step explanation: