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Math Help - Area in Matrices

  1. #1
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    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
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  2. #2
    Super Member Quacky's Avatar
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    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 \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?
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  3. #3
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    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
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  4. #4
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    Quote Originally Posted by terence View Post
    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.
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  5. #5
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    oh that makes it clearer. the 4 was that 'scale factor' I was talking about
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