## Problem on matrices as transformations

Let $A= \begin{pmatrix}1/2 & 0 \\ 0 & 2 \end{pmatrix}$.
How does the following shape get transformed by application of $A$:
• ## Solution

Recall that
We see $(1,0)$ gets shunk by half to $(1/2, 0)$.
We see $(0,1)$ gets scaled by two to $(0,2)$.
Graphically:
We see that the $x$ component gets cut in half, while the $y$ component is doubled. Hence the shape is transformed to: