Solution
= Solution
The three <linearly independent> <eigenvectors> still form a <basis>, so the same coefficient calculation applies to this <diagonalizable matrix> matrix. \b[The general solution is]
$$
\boxed{\mathbf x(t)=A_1e^{\lambda_1t}\mathbf e_1+e^{\lambda_2t}(A_2\mathbf e_2+A_3\mathbf e_3).}
$$
A repeated <eigenvalue> alone does not create a polynomial factor in time; that factor is needed only when a nontrivial <Jordan block> prevents a full eigenvector <basis>.