Answer
See solution
Work Step by Step
The area of the parallelogram is height times base length. Height is b and base length is c, so area is bc.
det$\begin{bmatrix}
a&c\\
b&0
\end{bmatrix}=-bc$
det$\begin{bmatrix}
c&a\\
0&b
\end{bmatrix}=bc$
Therefore, the magnitude of the determinant is the area of a parallelogram whose adjacent sides are u and v.
