= Solution
Take the switch-off time to be $t=0$. The state remains <continuous> through the source step, so $\mathbf y(0)=(1,1,1/4)^T$. Its eigendirection decomposition is
$$
\mathbf y(0)=(1,1,0)^T+\frac14(0,0,1)^T.
$$
The antisymmetric mode has zero amplitude because the first two initial components are equal. Applying the decay factors from part (b),
$$
\boxed{\mathbf y(t)=(e^{-t},\ e^{-t},\ \tfrac14e^{-4t})^T\qquad(t\geq0)}.
$$
The first two responses decay at rate one and the third at rate four, approaching the new zero-source <steady state>.
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