Thread: 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

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 which is the area of the transformed shape divided by the area of the original.

Did you have a specific example in mind?

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

Originally Posted by terence

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

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.

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