To visualize $T(x)=Ax$ on $\mathbb R^2$, transform the vertices and edges of a square or grid. For $A=\begin{bmatrix}1&1\\0&1\end{bmatrix}$, the unit square's vertices become $(0,0),(1,0),(2,1),(1,1)$. Straight edges remain straight, producing a sheared parallelogram.
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