Show that the span of \begin{bmatrix}1\\1\\0\\1\end{bmatrix} and \begin{bmatrix}1\\0\\2\\0\end{bmatrix} is a $T$-invariant subspace of the linear map given by
\begin{bmatrix}4&-2&-1&-1\\ 3&-1&-1&-1\\-2&2&2&0\\1&-1&0&1\end{bmatrix}
I tried to take some general vector in the span and multiply it by the matrix in the hope of getting something that was clearly a linear combination of my two original spanning vectors, but this did not work, that is, the vector was clearly not in the span.
So how am I meant to show $T$-invariance?
Note: Apologies for the formatting, my first time