Area of a linearly transformed curve

Geometry Level 4

Let $$C$$ be a closed curve in the $$xy$$ plane, with an enclosed area of $$A$$. The points on this curve are operated on by a linear transform, given by $$\mathbf{y = T x}$$, where $$\mathbf{x}$$ is the vector representing any point on $$C$$, and $$\mathbf{y}$$ is the vector of the its image, and matrix $$T$$ is given by

$$T = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix}$$

What will be the area of the transformed curve?

×