Given a rectangle R=[1,3] x [2,4], and the affin translation F : R^2 -> R^2 defined by F(x,y) = (1,3) + A*(x,y), where A is the 2x2 matrix (2 , 7 ; 3 , 1), what is the area of the affin transelation of the rectangle R?
The Attempt at a Solution
When I cross the vectors of R I get the scalar 2. Is this the area of R before we transelate it? The determinant of A equals 19, and 2*19=38. So this is my answer and it is wrong. Right answer is 76, so I guess the area of R before translation should be 76/det(A)=4. Where am I wrong?