Determinant and geometric representation

[shounakbhatta]

Hello,

Typically the area of a parallelogram if give by A=b*h

The det(M) =ad-bc, where m=2x2 matrix.

How they are related?

-- Shounak

 

[tiny-tim]

Hello Shounak!

If M is the matrix of a linear 2x2 transformation T,

then T will convert a square of area 1 into a parallelogram of area det(M).

(works also with volumes and 3x3 transformations, etc)

 

[shounakbhatta]

Hello Tim,

Thanks for the reply. I just want to confirm few things:

(1) Is the area of a parallelogram (abcd)= det(M), where M is a 2x2 matrix?

I am unable to understand what do you mean by 'T will convert to a square area 1'?

Can you please give me an example?

-- Shounak