Answer
See solution
Work Step by Step
The area of the parallelogram is the second entry of v multiplied by the difference of the entries of u, which is 6.
$\Bigg|
\begin{matrix}
3&1\\
0&2
\end{matrix}
\Bigg|=3\times2-0\times1=6$
They are equal.
When $u=\begin{bmatrix}
3\\
0
\end{bmatrix}$ and $v=\begin{bmatrix}
x\\
2
\end{bmatrix}$
Changing the first entry of v only performs a shear transformation of the parallelogram. Because it doesn't change its height or base length, the area doesn't change.
Likewise, $\Bigg|
\begin{matrix}
3&x\\
0&2
\end{matrix}
\Bigg|=3\times2-0\times x=6$
