1. ## Area in Matrices

I am reading my school's notes and I've got written down that to find the area in matrices, I should take the determinant,

Just to check if I am understanding well, the determinant that I should take should be of the transformation matrix?

and will the answer be directly the area ? or just a scale factor of the original?

thanks

2. What do you mean? If you have a matrix by itself, let's say M, then det(M) will give you the area. If you transform M into M', then det(M') will give you the area of M'

If you want to find the scale factor of enlargement, it will usually be $\displaystyle \frac{det(M')}{det(M)}$ which is the area of the transformed shape divided by the area of the original.

Did you have a specific example in mind?

3. qmm I get your point.

I was thinking for example you transform a square (2 units by 2 units ..from origin) by the matrix A below.
(4 3)
(2 2)

What would the new area be?

Det(A) or Det(A)*4

4. Originally Posted by terence

I was thinking for example you transform a square (2 units by 2 units ..from origin) by the matrix A below.
(4 3)
(2 2)

What would the new area be?

Det(A) or Det(A)*4
Det(A) gives you the area of the image of the unit square under the transformation. You want the area of the image of a 2x2 square, which will be Det(A)*4.

5. oh that makes it clearer. the 4 was that 'scale factor' I was talking about