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Determinant and geometric representation

  1. Nov 7, 2012 #1

    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
  2. jcsd
  3. Nov 7, 2012 #2


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    Hello Shounak! :smile:

    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). :wink:

    (works also with volumes and 3x3 transformations, etc)
  4. Nov 7, 2012 #3
    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
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