\begin{align*}
\vect{y}\in\rsp{A}
&\iff\vect{y}\in\csp{\transpose{A}}&&\knowl{./knowls/definition.RSM.knowl}{\text{Definition RSM}}\\
&\iff\linearsystem{\transpose{A}}{\vect{y}}\text{ is consistent}&&\knowl{./knowls/theorem.CSCS.knowl}{\text{Theorem CSCS}}
\end{align*}
The augmented matrix $\augmented{\transpose{A}}{\vect{y}}$ row reduces to
\begin{align*}
\begin{bmatrix}
\leading{1} & 0 & 0 & 0 \\
0 & \leading{1} & 0 & 0 \\
0 & 0 & \leading{1} & 0 \\
0 & 0 & 0 & \leading{1}
\end{bmatrix}
\end{align*}
and since the final column is a pivot column Theorem RCLS tells us the linear system is inconsistent and so $\vect{y}\not\in\rsp{A}$.