Given transformation matrix $$T=\begin{bmatrix}10&4\\3&8\end{bmatrix}$$
Applied to the points A(4,2) B(4,6) C(10,2) D(10,6) calculate the area of the resaulting figure.
So far I applied the transformation matrix to the given points:
\begin{bmatrix}10&4\\3&8\end{bmatrix}.\begin{bmatrix}4&4&10&10\\2&6&2&6\end{bmatrix} = \begin{bmatrix}48&64&108&124\\28&60&46&78\end{bmatrix} and the area before apllying transformation mtrix is 6×4=24 but I do not have any clue how to calculate the area after applying the transformation matrix, so, please help me and explain to me step by step how to find it.
[Math] Given transformation matrix, what is the area of the resulting figure
linear algebralinear-transformationsmatrices
Best Answer
The determinant scales area by $|\det(T)|$, so you may just calculate the area of the figure in the domain.
The original figure is a rectangle with area $4(6)=24$. Your determinant is $68$. So the area of the resulting figure is $$ 68(24)=1632 $$