The linear transformation $\ltdefn{T}{\complex{4}}{\complex{3}}$ is not injective. Find two inputs $\vect{x},\,\vect{y}\in\complex{4}$ that yield the same output (that is $\lt{T}{\vect{x}}=\lt{T}{\vect{y}}$). \begin{equation*} \lt{T}{\colvector{x_1\\x_2\\x_3\\x_4}}= \colvector{ 2x_1+x_2+x_3\\ -x_1+3x_2+x_3-x_4\\ 3x_1+x_2+2x_3-2x_4 } \end{equation*}