What is the area of the image of the rectangle [2..4]X[2..5] under the action of this matrix?
$\begin{bmatrix}2&3\\4&-1\end{bmatrix}$
The det of the matrix is -14, but I don't understand what this: [2..4]X[2..5] means. Somehow the area of that is 6 and the total area is -14*6 = -84
It's just left and right boundary along each axis. The rectangle starts at x=2 and ends at x=4, and vertically, it extends between y=2 and y=5, so the dimensions are $(4-2)\times(5-2)$.